Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

Invariant theory in exterior algebras and Amitsur-Levitzki type theorems

This article discusses invariant theories in some exterior algebras, which are closely related to Amitsur-Levitzki type theorems. First we consider the exterior algebra on the vector space of square matrices of size $n$, and look at the invariants under conjugations. We see that the algebra of these invariants is isomorphic to the exterior algebra on an $n$-dimensional vector space. Moreover we give a Cayley-Hamilton type theorem for these invariants (the anticommutative version of the Cayley-Hamilton theorem). This Cayley-Hamilton type theorem can also be regarded as a refinement of the Amits…

Dzhumadildaev括号：对易子的隐藏超对称性与Amitsur-Levitzki型恒等式

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

本文综述了Amitsur–Levitzki恒等式在各类李代数、李超代数中的推广成果，介绍了Dzhumadildaev通过反对称化子代数发现对易子隐藏超对称性的研究，并提出了相关开放问题。

On Kostant's theorem for the Lie superalgebra Q(n)

In this paper we study finite W-algebras for basic classical superalgebras and Q(n) associated to the regular even nilpotent coadjoint orbits. We prove that this algebra satisfies the Amitsur-Levitzki identity and therefore all its irreducible representations are finite-dimensional. In the case of Q(n) we give an explicit description of the W-algebra in terms of generators and relation and realize it as a quotient of the super-Yangian of Q(1).