Orthosymplectic Jordan superalgebras and~the~Wedderburn principal theorem

F. A. Gómez González ; R. Velásquez

Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 19-33.

Résumé

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.

Détail

Mots-clés : Jordan superalgebras, Wedderburn theorem.

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