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 $\mathcal{A}/\mathcal{N}\cong\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})$-bimodules contained in $\mathcal{N}$, and show with counter-examples that these restrictions cannot be weakened.
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