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Algebra and Discrete Mathematics, 2018, Volume 26, Issue 1, Pages 19–33
(Mi adm667)
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This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem
F. A. Gómez González, R. Velásquez Universidad de Antioquia, Calle 67 No. 53-108 Bloque 6-7 of. 337, Medellín, Antioquia, Colombia
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.
Keywords:
Jordan superalgebras, Wedderburn theorem.
Received: 02.11.2016 Revised: 19.01.2017
Citation:
F. A. Gómez González, R. Velásquez, “Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem”, Algebra Discrete Math., 26:1 (2018), 19–33
Linking options:
https://www.mathnet.ru/eng/adm667 https://www.mathnet.ru/eng/adm/v26/i1/p19
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