THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA 𝔬𝔰𝔭(1, 2n)

Abstract

Communicated by Ian M. MussonBased on Kostant's cohomological interpretation of the Amitsur-Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras osp(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur-Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.

Supertrace and Superquadratic Lie Structure on the Weyl Algebra, and Applications to Formal Inverse Weyl Transform

“…This embedding was also described in [13] and [8]. We give the proof in [8]: Definition 2.2. The twisted adjoint action of the Lie superalgebra W on itself is defined as:…”

“…[7]) and it was used for instance to develop singleton Anti-de-Sitter theories [7]. This embedding was also described in [13] and [8]. We give the proof in [8]: Definition 2.2.…”

“…Briefly, in a deformation quantization framework (see [3,17]), we quantize the natural Poisson bracket in an explicit way (Moyal ⋆-product). The main advantage of this quantization is the fact of being invariant with respect to the natural embedding of the Lie superalgebra osp (1, 2n) in W ( [7,13,8]), i.e. with respect to the orthosymplectic supersymmetry.…”