Associative superalgebras with homogeneous symmetric structures

Imen Ayadi; Saïd Benayadi

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arXiv · 1011.3002

Associative superalgebras with homogeneous symmetric structures

Imen Ayadi·Saïd Benayadi

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Abstract

A homogeneous symmetric structure on an associative superalgebra A is a non-degenerate, supersymmetric, homogeneous (i.e. even or odd) and associative bilinear form on A. In this paper, we show that any associative superalgebra with non null product can not admit simultaneously even-symmetric and odd-symmetric structure. We prove that all simple associative superalgebras admit either even-symmetric or odd-symmetric structure and we give explicitly, in every case, the homogeneous symmetric structures. We introduce some notions of generalized double extensions in order to give inductive descriptions of even-symmetric associative superalgebras and odd-symmetric associative superalgebras. We obtain also an other interesting description of odd-symmetric associative superalgebras whose even parts are semi-simple bimodules without using the notions of double extensions.

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BibTeX RIS

Imen Ayadi, Saïd Benayadi. 2010-11-12. Associative superalgebras with homogeneous symmetric structures. https://arxiv.org/abs/1011.3002

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