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arXiv · 1709.08465

Wedderburn principal theorem for Jordan superalgebras I

F. A. Gómez-González
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Abstract

We consider finite dimensional Jordan superalgebras $\jor$ over an algebraically closed field of characteristic 0, with solvable radical $\rad$ such that $\radd=0$ and $\jor/\rad$ is a simple Jordan superalgebra of one of the following types: Kac $\kac$, Kaplansky $\mathcal{K}_3$ superform or $\algdt$. We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subsuperbimodules of $N$ are imposed, where $N$ is considered as a $J$-superbimodule, and $J$ is a simple Jordan superalgebra. Using counterexamples, it is shown that the imposed restrictions are essential.

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F. A. Gómez-González. 2017-09-25. Wedderburn principal theorem for Jordan superalgebras I. https://arxiv.org/abs/1709.08465

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