Symmetric Zinbiel superalgebras
Rings and Algebras
2022-08-02 v1
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.
Cite
@article{arxiv.2203.00311,
title = {Symmetric Zinbiel superalgebras},
author = {Saïd Benayadi and Ivan Kaygorodov and Fahmi Mhamdi},
journal= {arXiv preprint arXiv:2203.00311},
year = {2022}
}