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arXiv · 2203.00311

Symmetric Zinbiel superalgebras

Saïd Benayadi·Ivan Kaygorodov·Fahmi Mhamdi
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Abstract

The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index of a symmetric Zinbiel superalgebra is not greater than 4 and describe two-generated symmetric Zinbiel algebras and odd generated superalgebras. We discuss identities of mono and binary symmetric Zinbiel and Leibniz algebras. It is proven that each quadratic Zinbiel algebra is 2-step nilpotent. Also, we study double extensions of symmetric Zinbiel algebras.

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Saïd Benayadi, Ivan Kaygorodov, Fahmi Mhamdi. 2022-03-01. Symmetric Zinbiel superalgebras. https://doi.org/10.1080/00927872.2022.2096224

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