Paper detail

The Dzhumadildaev brackets: a hidden supersymmetry of commutators and the Amitsur-Levitzki-type identities

The Amitsur-Levitzki identity for matrices was generalized in several directions: by Kostant for simple finite-dimensional Lie algebras, by Kirillov (later joined by Kontsevich, Molev, Ovsienko, and Udalova) for simple vectorial Lie algebras with polynomial coefficients, and by Gie, Pinczon, and Ushirobira for the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|n)$. Dzhumadildaev switched the focus of attention in these results by considering the algebra formed by antisymmetrizors and discovered a hidden supersymmetry of commutators. We overview these results and their possible generalizations (open problems).

preprint2019arXivOpen access

Signal facts

What is known right now

Open access2 authors1 topic

Next steps

Decide what to do with this paper

Use like or dislike for the fast social read. The more specific scholarly feedback stays available below when needed.

Log in to curate

Reading frame

Keep the important context close to the paper

Keep the important signals around this paper in one place: votes, save state, collection context, reviews and the metadata you need before deciding what to do next.

Institutions

Add specific reaction

Move through the context

Research map

Open full explorer

Move through nearby people, institutions, topics and adjacent work without leaving the paper page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Structured reviews

0 review(s)

ContributeLeave structured feedbackUse the review template when you have a concrete strength, concern or method question.Open review form

No structured reviews yet. High-signal critique starts here.

Work discussion

0 comment(s)

DiscussAdd a high-signal commentKeep quick notes, caveats and replication pointers separate from formal reviews.Open comment form

No discussion yet. The first strong comment sets the tone.