Irreductible Representations of the Simple Jordan Superalgebra of Grassmann Poisson bracket

Abstract

We obtain classification of the irreducible bimodules over the Jordan superalgebra $Kan(n)$, the Kantor double of the Grassmann Poisson superalgebra $G_n$ on $n$ odd generators, for all $n\ge 2$ and an algebraically closed field of characteristic $\ne 2$. This generalizes the corresponding result of C.Martínez and E.Zelmanov announced in \cite{MZ2} for $n>4$ and a field of characteristic zero.}