Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem (WPT)

TL;DR

This paper investigates an analogue of the Wedderburn principal theorem for finite dimensional Jordan superalgebras with specific radical properties, establishing conditions for the theorem's validity and providing counterexamples for its limitations.

Contribution

It extends the Wedderburn principal theorem to certain Jordan superalgebras, identifying necessary restrictions and demonstrating their sharpness with counterexamples.

Findings

WPT holds under specific restrictions on bimodules

Counterexamples show restrictions cannot be weakened

Provides conditions for the validity of WPT in Jordan superalgebras

Abstract

An analogue of the Wedderbur principal theorem (WPT) is considered for finite dimensional Jordan superalgebras A with solvable radical N, such that N^2=0 and A/N is isomorphic to Josp_n|2m(F), where F is an algebraicallly closed field of characteristic zero. Let's we prove that the WPT is valid under some restrictions over the irreducible Josp_n|2m(F)-bimodules contained in N, and it is shown with counter-examples that these restrictions can not be weakened.