Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem

Abstract

An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superalgebras \(\mathcal{A}\) with solvable radical \(\mathcal{N}\), \(\mathcal{N}^2=0\), and such that \(\mathcal{A}/\mathcal{N}\cong\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\), where \(\mathbb{F}\) is a field of characteristic zero.We prove that the WPT is valid under some restrictions over the irreducible \(\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\)-bimodules contained in \(\mathcal{N}\), and show with counter-examples that these restrictions cannot be weakened.