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

Pierre-Alexandre Gie (1) , Georges Pinczon (1) , Rosane Ushirobira (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).

Domaines: Théorie des représentations [math.RT]

Pierre-Alexandre Gie, Georges Pinczon, Rosane Ushirobira. Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n). Letters in Mathematical Physics, 2003, pp.14. ⟨10.1023/B:MATH.0000017702.95884.c0⟩. ⟨hal-00438547⟩