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arXiv · 2008.04889

Gröbner-Shirshov bases theory and extensions of Leibniz superalgebras

Yuxiu Bai·Yuqun Chen
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Abstract

In this paper, we elaborate Gröbner-Shirshov bases method for Leibniz (super)algebras. We show that there is a unique reduced Gröbner-Shirshov basis for every (graded) ideal of a free Leibniz (super)algebra. As applications, we construct linear bases of free metabelian Leibniz superalgebras and new linear bases of free metabelian Lie algebras. We present a complete characterization of extensions of a Leibniz (super)algebra by another Leibniz (super)algebra, where the former is presented by generators and relations.

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Yuxiu Bai, Yuqun Chen. 2020-08-08. Gröbner-Shirshov bases theory and extensions of Leibniz superalgebras. https://arxiv.org/abs/2008.04889

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