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Haisheng Li

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math.QA Computer Vision math.RT eess.IV hep-th Artificial Intelligence Information Retrieval Machine Learning

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preprint2026arXiv

Robust Lightweight Crack Classification for Real-Time UAV Bridge Inspection

With the widespread application of Unmanned Aerial Vehicles (UAVs) in bridge structural health monitoring, deep learning-based automatic crack detection has become a major research focus. However, practical UAV inspections still face four key challenges: weak crack features, degraded imaging conditions, severe class imbalance, and limited computational resources for practical UAV inspection workflows. To address these issues, this paper proposes a unified lightweight convolutional neural network framework composed of four synergistic components: a lightweight backbone network, a Convolutional Block Attention Module (CBAM) for channel and spatial enhancement, a directed robust augmentation strategy based on inspection-scene priors, and Focal Loss for hard-sample learning under class imbalance. Experiments on the SDNET2018 bridge deck dataset show that the proposed method achieves an inference speed of 825 FPS with only 11.21M parameters and 1.82G FLOPs. Compared with the baseline model, the complete framework improves the F1-score by 2.51% and recall by 3.95%. In addition, Grad-CAM visualizations indicate that the introduced attention module shifts the model's focus from scattered regions to precise tracking along crack trajectories. Overall, this study achieves a strong balance among accuracy, speed, and robustness, providing a practical solution for ground-station assisted real-time deployment in UAV bridge inspections. The source code is available at: https://github.com/skylynf/AttXNet .

preprint2022arXiv

A review on vision-based analysis for automatic dietary assessment

Background: Maintaining a healthy diet is vital to avoid health-related issues, e.g., undernutrition, obesity and many non-communicable diseases. An indispensable part of the health diet is dietary assessment. Traditional manual recording methods are not only burdensome but time-consuming, and contain substantial biases and errors. Recent advances in Artificial Intelligence (AI), especially computer vision technologies, have made it possible to develop automatic dietary assessment solutions, which are more convenient, less time-consuming and even more accurate to monitor daily food intake. Scope and approach: This review presents Vision-Based Dietary Assessment (VBDA) architectures, including multi-stage architecture and end-to-end one. The multi-stage dietary assessment generally consists of three stages: food image analysis, volume estimation and nutrient derivation. The prosperity of deep learning makes VBDA gradually move to an end-to-end implementation, which applies food images to a single network to directly estimate the nutrition. The recently proposed end-to-end methods are also discussed. We further analyze existing dietary assessment datasets, indicating that one large-scale benchmark is urgently needed, and finally highlight critical challenges and future trends for VBDA. Key findings and conclusions: After thorough exploration, we find that multi-task end-to-end deep learning approaches are one important trend of VBDA. Despite considerable research progress, many challenges remain for VBDA due to the meal complexity. We also provide the latest ideas for future development of VBDA, e.g., fine-grained food analysis and accurate volume estimation. This review aims to encourage researchers to propose more practical solutions for VBDA.

preprint2022arXiv

BCS-Net: Boundary, Context and Semantic for Automatic COVID-19 Lung Infection Segmentation from CT Images

The spread of COVID-19 has brought a huge disaster to the world, and the automatic segmentation of infection regions can help doctors to make diagnosis quickly and reduce workload. However, there are several challenges for the accurate and complete segmentation, such as the scattered infection area distribution, complex background noises, and blurred segmentation boundaries. To this end, in this paper, we propose a novel network for automatic COVID-19 lung infection segmentation from CT images, named BCS-Net, which considers the boundary, context, and semantic attributes. The BCS-Net follows an encoder-decoder architecture, and more designs focus on the decoder stage that includes three progressively Boundary-Context-Semantic Reconstruction (BCSR) blocks. In each BCSR block, the attention-guided global context (AGGC) module is designed to learn the most valuable encoder features for decoder by highlighting the important spatial and boundary locations and modeling the global context dependence. Besides, a semantic guidance (SG) unit generates the semantic guidance map to refine the decoder features by aggregating multi-scale high-level features at the intermediate resolution. Extensive experiments demonstrate that our proposed framework outperforms the existing competitors both qualitatively and quantitatively.

preprint2022arXiv

Boundary Guided Semantic Learning for Real-time COVID-19 Lung Infection Segmentation System

The coronavirus disease 2019 (COVID-19) continues to have a negative impact on healthcare systems around the world, though the vaccines have been developed and national vaccination coverage rate is steadily increasing. At the current stage, automatically segmenting the lung infection area from CT images is essential for the diagnosis and treatment of COVID-19. Thanks to the development of deep learning technology, some deep learning solutions for lung infection segmentation have been proposed. However, due to the scattered distribution, complex background interference and blurred boundaries, the accuracy and completeness of the existing models are still unsatisfactory. To this end, we propose a boundary guided semantic learning network (BSNet) in this paper. On the one hand, the dual-branch semantic enhancement module that combines the top-level semantic preservation and progressive semantic integration is designed to model the complementary relationship between different high-level features, thereby promoting the generation of more complete segmentation results. On the other hand, the mirror-symmetric boundary guidance module is proposed to accurately detect the boundaries of the lesion regions in a mirror-symmetric way. Experiments on the publicly available dataset demonstrate that our BSNet outperforms the existing state-of-the-art competitors and achieves a real-time inference speed of 44 FPS.

preprint2022arXiv

Regular representations and $A_{n}(V)$ - $A_{m}(V)$ bimodules

This paper is to establish a natural connection between regular representations for a vertex operator algebra $V$ and $A_{n}(V)$ - $A_{m}(V)$ bimodules of Dong and Jiang. Let $W$ be a weak $V$ -module and let $(m,n)$ be a pair of nonnegative integers. We study two quotient spaces $A_{n,m}^{\dagger}(W)$ and $A^{\diamond}_{n,m}(W)$ of $W$ . It is proved that the dual space $A^{\dagger}_{n,m}(W)^{*}$ viewed as a subspace of $W^*$ coincides with the level- $(m,n)$ vacuum subspace of the regular representation module $\mathfrak{D}_{(-1)}(W)$ . By making use of this connection, we obtain an $A_{n}(V)$ - $A_m(V)$ bimodule structure on both $A_{n,m}^{\dagger}(W)$ and $A^{\diamond}_{n,m}(W)$ . Furthermore, we obtain an $\N$ -graded weak $V$ -module structure together with a commuting right $A_m(V)$ -module structure on $A^{\diamond}_{\Box,m}(W):=\oplus_{n\in \N}A^{\diamond}_{n,m}(W)$ . Consequently, we recover the corresponding results and roughly confirm a conjecture of Dong and Jiang.

preprint2022arXiv

Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras

In this paper, we study a family of infinite-dimensional Lie algebras $\widehat{X}_{S}$ , where $X$ stands for the type: $A,B,C,D$ , and $S$ is an abelian group, which generalize the $A,B,C,D$ series of trigonometric Lie algebras. Among the main results, we identify $\widehat{X}_{S}$ with what are called the covariant algebras of the affine Lie algebra $\widehat{\mathcal{L}_{S}}$ with respect to some automorphism groups, where $\mathcal{L}_{S}$ is an explicitly defined associative algebra viewed as a Lie algebra. We then show that restricted $\widehat{X}_{S}$ -modules of level $\ell$ naturally correspond to equivariant quasi modules for affine vertex algebras related to $\mathcal{L}_{S}$ . Furthermore, for any finite cyclic group $S$ , we completely determine the structures of these four families of Lie algebras, showing that they are essentially affine Kac-Moody Lie algebras of certain types.

preprint2022arXiv

Twisted regular representations of vertex operator algebras

This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $σ_1,σ_2$ be commuting finite-order automorphisms of $V$ and let $σ=(σ_1σ_2)^{-1}$ . Among the main results, for any $σ$ -twisted $V$ -module $W$ and any nonzero complex number $z$ , we construct a weak $σ_1\otimes σ_2$ -twisted $V\otimes V$ -module $\mathfrak{D}_{σ_1,σ_2}^{(z)}(W)$ inside $W^{*}$ . Let $W_1,W_2$ be $σ_1$ -twisted, $σ_2$ -twisted $V$ -modules, respectively. We show that $P(z)$ -intertwining maps from $W_1\otimes W_2$ to $W^{*}$ are the same as homomorphisms of weak $σ_1\otimes σ_2$ -twisted $V\otimes V$ -modules from $W_1\otimes W_2$ into $\mathfrak{D}_{σ_1,σ_2}^{(z)}(W)$ . We also show that a $P(z)$ -intertwining map from $W_1\otimes W_2$ to $W^{*}$ is equivalent to an intertwining operator of type $\binom{W'}{W_1\; W_2}$ , which is a twisted version of a result of Huang and Lepowsky. Finally, we show that for each $τ$ -twisted $V$ -module $M$ with $τ$ any finite-order automorphism of $V$ , the coefficients of the $q$ -graded trace function lie in $\mathfrak{D}_{τ,τ^{-1}}^{(-1)}(V)$ , which generate a $τ\otimes τ^{-1}$ -twisted $V\otimes V$ -submodule isomorphic to $M\otimes M'$ .

preprint2021arXiv

Toroidal extended affine Lie algebras and vertex algebras

In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $ϕ$ -coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and $ϕ$ -coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of irreducible modules for the variant Lie algebras.

preprint2020arXiv

Extended affine Lie algebras, vertex algebras, and reductive groups

In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple affine vertex algebra $L_{\widehat{sl_{\infty}}}(\ell,0)$ with $\ell$ a positive integer, and Levi subgroups $G$ of $GL_\ell(\mathbb{C})$ . First, we give a canonical isomorphism between the category of integrable restricted $\widehat{sl_N}(\mathbb{C}_q)$ -modules of level $\ell$ and that of equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$ -modules. Second, we classify irreducible $\mathbb{N}$ -graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$ -modules. Third, we establish a duality between irreducible $\mathbb{N}$ -graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$ -modules and irreducible regular $G$ -modules on certain fermionic Fock spaces. Fourth, we obtain an explicit realization of every irreducible $\mathbb{N}$ -graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$ -module. Fifth, we completely determine the following branchings: 1 The branching from $L_{\widehat{sl_{\infty}}}(\ell,0)\otimes L_{\widehat{sl_{\infty}}}(\ell',0)$ to $L_{\widehat{sl_{\infty}}}(\ell+\ell',0)$ for quasi modules. 2 The branching from $\widehat{sl_N}(\mathbb{C}_q)$ to its Levi subalgebras. 3 The branching from $\widehat{sl_N}(\mathbb{C}_q)$ to its subalgebras $\widehat{sl_N}(\mathbb{C}_q[t_0^{\pm M_0},t_1^{\pm M_1}])$ .

preprint2020arXiv

Shape retrieval of non-rigid 3d human models

3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. We extend our recent paper which provided a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models. This benchmark provided a far stricter challenge than previous shape benchmarks. We have added 145 new models for use as a separate training set, in order to standardise the training data used and provide a fairer comparison. We have also included experiments with the FAUST dataset of human scans. All participants of the previous benchmark study have taken part in the new tests reported here, many providing updated results using the new data. In addition, further participants have also taken part, and we provide extra analysis of the retrieval results. A total of 25 different shape retrieval methods.

preprint2016arXiv

$ϕ$ -coordinated modules for quantum vertex algebras and associative algebras

We study $\N$ -graded $ϕ$ -coordinated modules for a general quantum vertex algebra $V$ of a certain type in terms of an associative algebra $\widetilde{A}(V)$ introduced by Y.-Z. Huang. Among the main results, we establish a bijection between the set of equivalence classes of irreducible $\N$ -graded $ϕ$ -coordinated $V$ -modules and the set of isomorphism classes of irreducible $\widetilde{A}(V)$ -modules. We also show that for a vertex operator algebra, rationality, regularity, and fusion rules are independent of the choice of the conformal vector.

preprint2016arXiv

Remarks on $ϕ$ -coordinated modules for quantum vertex algebras

This paper is about $ϕ$ -coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $ϕ$ -coordinated modules for different $ϕ$ are established. For vertex operator algebras, a reinterpretation of Frenkel-Huang-Lepowsky's theorem on contragredient module is given in terms of $ϕ$ -coordinated modules.

preprint2015arXiv

Certain Clifford-like algebra and quantum vertex algebras

In this paper, we study in the context of quantum vertex algebras a certain Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW type and classify its $\mathbb N$ -graded irreducible modules by using a notion of Verma module. On the other hand, we introduce a new algebra, a twin of the original algebra. Using this new algebra we construct a quantum vertex algebra and we associate $\mathbb N$ -graded modules for Jing-Nie's Clifford-like algebra with $ϕ$ -coordinated modules for the quantum vertex algebra. We also show that the adjoint module for the quantum vertex algebra is irreducible.

preprint2015arXiv

Heisenberg VOAs over Fields of Prime Characteristic and Their Representations

In this paper, we study Heisenberg vertex algebras over fields of prime characteristic. The new feature is that the Heisenberg vertex algebras are no longer simple unlike in the case of characteristic zero. We then study a family of simple quotient vertex algebras and we show that for each such simple quotient vertex algebra, irreducible modules are unique up to isomorphism and every module is completely reducible. To achieve our goal, we also establish a complete reducibility theorem for a certain category of modules over Heisenberg algebras.

preprint2015arXiv

Twisted modules for Toroidal vertex algebras

This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that almost all extended affine Lie algebras can be associated to toroidal vertex algebras.

preprint2014arXiv

$q$ -Virasoro algebra and vertex algebras

In this paper, we study a certain deformation $D$ of the Virasoro algebra that was introduced and called $q$ -Virasoro algebra by Nigro,in the context of vertex algebras. Among the main results, we prove that for any complex number $\ell$ , the category of restricted $D$ -modules of level $\ell$ is canonically isomorphic to the category of quasi modules for a certain vertex algebra of affine type. We also prove that the category of restricted $D$ -modules of level $\ell$ is canonically isomorphic to the category of $\mathbb{Z}$ -equivariant $ϕ$ -coordinated quasi modules for the same vertex algebra. In the process, we introduce and employ a certain infinite dimensional Lie algebra which is defined in terms of generators and relations and then identified explicitly with a subalgebra of $\mathfrak{gl}_{\infty}$ .

preprint2014arXiv

$ϕ_ε$ -coordinated modules for vertex algebras

We study $ϕ_ε$ -coordinated modules for vertex algebras, where $ϕ_ε$ with $ε$ an integer parameter is a family of associates of the one-dimensional additive formal group. As the main results, we obtain a Jacobi type identity and a commutator formula for $ϕ_ε$ -coordinated modules. We then use these results to study $ϕ_ε$ -coordinated modules for vertex algebras associated to Novikov algebras by Primc.

preprint2014arXiv

Simple Toroidal Vertex Algebras and Their Irreducible Modules

In this paper, we continue the study on toroidal vertex algebras initiated in \cite{LTW}, to study concrete toroidal vertex algebras associated to toroidal Lie algebra $L_{r}(\hat{\frak{g}})=\hat{\frak{g}}\otimes L_r$ , where $\hat{\frak{g}}$ is an untwisted affine Lie algebra and $L_r=$ \mathbb{C}[t_{1}^{\pm 1},\ldots,t_{r}^{\pm 1}] $. We first construct an$ (r+1) $-toroidal vertex algebra$ V(T,0) $and show that the category of restricted$ L_{r}(\hat{\frak{g}}) $-modules is canonically isomorphic to that of$ V(T,0) $-modules.Let$ c $denote the standard central element of$ \hat{\frak{g}} $and set$ S_c=U(L_r(\mathbb{C}c)) $. We furthermore study a distinguished subalgebra of$ V(T,0) $, denoted by$ V(S_c,0) $. We show that (graded) simple quotient toroidal vertex algebras of$ V(S_c,0) $are parametrized by a$ \mathbb{Z}^r $-graded ring homomorphism$ ψ:S_c\rightarrow L_r $such that Im$ ψ $is a$ \mathbb{Z}^r $-graded simple$ S_c $-module. Denote by$ L(ψ,0} $the simple$ (r+1) $-toroidal vertex algebra of$ V(S_c,0) $associated to$ ψ $. We determine for which$ ψ $,$ L(ψ,0) $is an integrable$ L_{r}(\hat{\frak{g}}) $-module and we then classify irreducible$ L(ψ,0) $-modules for such a$ ψ$. For our need, we also obtain various general results.

preprint2013arXiv

Associating quantum vertex algebras to Lie algebra $\gl_{\infty}$

In this paper, we present a canonical association of quantum vertex algebras and their $ϕ$ -coordinated modules to Lie algebra $\gl_{\infty}$ and its 1-dimensional central extension. To this end we construct and make use of another closely related infinite-dimensional Lie algebra.

preprint2013arXiv

On a category of $gl_{\infty}$ -modules

We study a particular category ${\cal{C}}$ of $\gl_{\infty}$-modules and a subcategory ${\cal{C}}_{int}$ of integrable $\gl_{\infty}$-modules. As the main results, we classify the irreducible modules in these two categories and we show that every module in category ${\cal{C}}_{int}$ is semi-simple. Furthermore, we determine the decomposition of the tensor products of irreducible modules in category ${\cal{C}}_{int}$ .

preprint2013arXiv

On quasi modules at infinity for vertex algebras

A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in \cite{li-infinity}. In this current paper, quasi modules at infinity for vertex algebras are revisited. Among the main results, we extend some technical results, to fill in a gap in the proof of a theorem therein, and we obtain a commutator formula for general quasi modules at infinity and establish a version of the converse of the aforementioned theorem.

preprint2012arXiv

$G$ -covariant $ϕ$ -coordinated quasi modules for quantum vertex algebras

This is a paper in a series to study quantum vertex algebras and their relations with various quantum algebras. In this paper, we introduce a notion of T-type quantum vertex algebra and a notion of $G$ -covariant $ϕ$ -coordinated quasi module for a $T$ -type quantum vertex algebra with an automorphism group $G$ . We refine and extend several previous results and we obtain a commutator formula for $G$ -covariant $ϕ$ -coordinated quasi modules. As an illustrating example, we study a special case of the deformed Virasoro algebra $\V_{p,q}$ with $q=-1$ , to which we associate a Clifford vertex superalgebra and its $G$ -covariant $ϕ$ -coordinated quasi modules.

preprint2012arXiv

On vertex Leibniz algebras

In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without vacuum can be naturally extended to a vertex algebra. On the other hand, we show that a vertex Leibniz algebra can be embedded into a vertex algebra if and only if it admits a faithful module. To each vertex Leibniz algebra we associate a vertex algebra without vacuum which is universal to the forgetful functor. Furthermore, from any Leibniz algebra $\g$ we construct a vertex Leibniz algebra $V_{\g}$ and show that $V_{\g}$ can be embedded into a vertex algebra if and only if $\g$ is a Lie algebra.

preprint2012arXiv

Toroidal vertex algebras and their modules

We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal Lie algebras.

preprint2011arXiv

Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras

We associate quantum vertex algebras and their $ϕ$ -coordinated quasi modules to certain deformed Heisenberg algebras.

preprint2011arXiv

Twisted tensor products of nonlocal vertex algebras

In this paper we introduce and study a twisted tensor product construction of nonlocal vertex algebras. Among the main results, we establish a universal property and give a characterization of a twisted tensor product. Furthermore, we give a construction of modules for a twisted tensor product. We also show that smash products studied by one of us before can be realized as twisted tensor products.

preprint2010arXiv

$\hbar$ -adic quantum vertex algebras and their modules

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of $\hbar$ -adic nonlocal vertex algebra and $\hbar$ -adic (weak) quantum vertex algebra, slightly generalizing Etingof-Kazhdan's notion of quantum vertex operator algebra. For any topologically free $\C[[\h]]$-module $W$ , we study $\hbar$ -adically compatible subsets and $\hbar$ -adically $§$ -local subsets of $(\End W)[[x,x^{-1}]]$. We prove that any $\hbar$ -adically compatible subset generates an $\hbar$ -adic nonlocal vertex algebra with $W$ as a module and that any $\hbar$ -adically $§$ -local subset generates an $\hbar$ -adic weak quantum vertex algebra with $W$ as a module. A general construction theorem of $\hbar$ -adic nonlocal vertex algebras and $\hbar$ -adic quantum vertex algebras is obtained. As an application we associate the centrally extended double Yangian of $\sl_{2}$ to $\hbar$ -adic quantum vertex algebras.

preprint2010arXiv

Quantum vertex $F((t))$ -algebras and their modules

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras with $\F$ a field of characteristic zero and $t$ a formal variable, and we give a conceptual construction of (weak) quantum vertex $\F((t))$-algebras and their modules. As an application, we associate weak quantum vertex $\F((t))$-algebras to quantum affine algebras, providing a solution to a problem posed by Frenkel and Jing. We also explicitly construct an example of quantum vertex $\F((t))$-algebras from a certain quantum $βγ$ -system.

preprint2010arXiv

Quantum vertex algebras and their phi-coordinated quasi modules

We develop a theory of $ϕ$ -coordinated (quasi) modules for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their $ϕ$ -coordinated (quasi) modules, where $ϕ$ is what we call an associate of the one-dimensional additive formal group. By specializing $ϕ$ to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of \cite{li-qva1}. As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum vertex algebras and $ϕ$ -coordinated modules to a certain quantum $βγ$ -system.

preprint2010arXiv

Twisted modules and pseudo-endomorphisms

We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary modules by pseudo-endomorphisms, which are intrinsically connected to one of the two constructions.

preprint2010arXiv

Vertex $F$ -algebras and their $ϕ$ -coordinated modules

In this paper, for every one-dimensional formal group $F$ we formulate and study a notion of vertex $F$ -algebra and a notion of $ϕ$ -coordinated module for a vertex $F$ -algebra where $ϕ$ is what we call an associate of $F$ . In the case that $F$ is the additive formal group, vertex $F$ -algebras are exactly ordinary vertex algebras. We give a canonical isomorphism between the category of vertex $F$ -algebras and the category of ordinary vertex algebras. Meanwhile, for every formal group we completely determine its associates. We also study $ϕ$ -coordinated modules for a general vertex $\Z$ -graded algebra $V$ with $ϕ$ specialized to a particular associate of the additive formal group and we give a canonical connection between $V$ -modules and $ϕ$ -coordinate modules for a vertex algebra obtained from $V$ by Zhu's change-of-variables theorem.

preprint2009arXiv

On quantum vertex algebras and their modules

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras with quantum vertex algebras.

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Haisheng Li

Research overview

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32 publications

Robust Lightweight Crack Classification for Real-Time UAV Bridge Inspection

A review on vision-based analysis for automatic dietary assessment

BCS-Net: Boundary, Context and Semantic for Automatic COVID-19 Lung Infection Segmentation from CT Images

Boundary Guided Semantic Learning for Real-time COVID-19 Lung Infection Segmentation System

Regular representations and $A_{n}(V)$ - $A_{m}(V)$ bimodules

Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras

Twisted regular representations of vertex operator algebras

Toroidal extended affine Lie algebras and vertex algebras

Extended affine Lie algebras, vertex algebras, and reductive groups

Shape retrieval of non-rigid 3d human models

$ϕ$ -coordinated modules for quantum vertex algebras and associative algebras

Remarks on $ϕ$ -coordinated modules for quantum vertex algebras

Certain Clifford-like algebra and quantum vertex algebras

Heisenberg VOAs over Fields of Prime Characteristic and Their Representations

Twisted modules for Toroidal vertex algebras

$q$ -Virasoro algebra and vertex algebras

$ϕ_ε$ -coordinated modules for vertex algebras

Simple Toroidal Vertex Algebras and Their Irreducible Modules

Associating quantum vertex algebras to Lie algebra $\gl_{\infty}$

On a category of $gl_{\infty}$ -modules

On quasi modules at infinity for vertex algebras

$G$ -covariant $ϕ$ -coordinated quasi modules for quantum vertex algebras

On vertex Leibniz algebras

Toroidal vertex algebras and their modules

Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras

Twisted tensor products of nonlocal vertex algebras

$\hbar$ -adic quantum vertex algebras and their modules

Quantum vertex $F((t))$ -algebras and their modules

Quantum vertex algebras and their phi-coordinated quasi modules

Twisted modules and pseudo-endomorphisms

Vertex $F$ -algebras and their $ϕ$ -coordinated modules

On quantum vertex algebras and their modules

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Haisheng Li

Research overview

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32 publications

Robust Lightweight Crack Classification for Real-Time UAV Bridge Inspection

A review on vision-based analysis for automatic dietary assessment

BCS-Net: Boundary, Context and Semantic for Automatic COVID-19 Lung Infection Segmentation from CT Images

Boundary Guided Semantic Learning for Real-time COVID-19 Lung Infection Segmentation System

Regular representations and An(V)A_{n}(V)An​(V)-Am(V)A_{m}(V)Am​(V) bimodules

Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras

Twisted regular representations of vertex operator algebras

Toroidal extended affine Lie algebras and vertex algebras

Extended affine Lie algebras, vertex algebras, and reductive groups

Shape retrieval of non-rigid 3d human models

ϕϕϕ-coordinated modules for quantum vertex algebras and associative algebras

Remarks on ϕϕϕ-coordinated modules for quantum vertex algebras

Certain Clifford-like algebra and quantum vertex algebras

Heisenberg VOAs over Fields of Prime Characteristic and Their Representations

Twisted modules for Toroidal vertex algebras

qqq-Virasoro algebra and vertex algebras

ϕεϕ_εϕε​-coordinated modules for vertex algebras

Simple Toroidal Vertex Algebras and Their Irreducible Modules

Associating quantum vertex algebras to Lie algebra $\gl_{\infty}$

On a category of gl∞gl_{\infty}gl∞​-modules

On quasi modules at infinity for vertex algebras

GGG-covariant ϕϕϕ-coordinated quasi modules for quantum vertex algebras

On vertex Leibniz algebras

Toroidal vertex algebras and their modules

Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras

Twisted tensor products of nonlocal vertex algebras

ℏ\hbarℏ-adic quantum vertex algebras and their modules

Quantum vertex F((t))F((t))F((t))-algebras and their modules

Quantum vertex algebras and their phi-coordinated quasi modules

Twisted modules and pseudo-endomorphisms

Vertex FFF-algebras and their ϕϕϕ-coordinated modules

On quantum vertex algebras and their modules

See the researcher in context

Building this map preview

Regular representations and $A_{n}(V)$ - $A_{m}(V)$ bimodules

$ϕ$ -coordinated modules for quantum vertex algebras and associative algebras

Remarks on $ϕ$ -coordinated modules for quantum vertex algebras

$q$ -Virasoro algebra and vertex algebras

$ϕ_ε$ -coordinated modules for vertex algebras

On a category of $gl_{\infty}$ -modules

$G$ -covariant $ϕ$ -coordinated quasi modules for quantum vertex algebras

$\hbar$ -adic quantum vertex algebras and their modules

Quantum vertex $F((t))$ -algebras and their modules

Vertex $F$ -algebras and their $ϕ$ -coordinated modules