Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem

Abstract

An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superal-gebras A with solvable radical N, N² = 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. Introduction