Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem

Abstract

An analogue of the Wedderburn Principal The- orem (WPT) is considered for finite-dimensional Jordan superal- gebras A with solvable radical N , N 2 = 0, and such that A/N ∼=

Jospn|2m(F), where F is a field of characteristic zero. We prove that the WPT is valid under some restrictions over the irreducible Jospn|2m(F)-bimodules contained in N , and show with counter-examples that these restrictions cannot be weakened.