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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2018, том 26, выпуск 1, страницы 19–33 (Mi adm667)

Эта публикация цитируется в 2 статьях

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

Аннотация: 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.

Ключевые слова: Jordan superalgebras, Wedderburn theorem.

MSC: 17C70, 17C27, 17C55

Поступила в редакцию: 02.11.2016
Исправленный вариант: 19.01.2017

Язык публикации: английский



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