Jordan super algebras of type $JP_n$, $n\geq 3$ and the Wedderburn principal theorem

Abstract

We investigate an analogue to the Wedderburn Principal Theorem (WPT) for a finite-dimensional Jordan superalgebra $J$ with solvable radical $N$ such that $N^2=0$ and $J/N\cong JP_n$, $n\geq 3$. We consider $N$ as an irreducible $JP_n$-bimodule and we prove that the WPT holds for $J$.