Abstract crystals for quantum Borcherds-Bozec algebras

In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of ${B}(\infty)$ and ${B}(λ)$ as its application, where ${B}(\infty)$ and ${B}(λ)$ are the crystals of the negative half part of the quantum Borcherds-Bozec algebra $U_q(\mathfrak g)$ and its irreducible highest weight module $V(λ)$, respectively.

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