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arXiv · 1603.01454

Extensions of associative and Lie algebras via Gr\"obner-Shirshov bases method

Yuqun Chen·Jianjun Qiu
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Abstract

Let $\mathfrak{a},\mathfrak{b},\mathfrak{e}$ be algebras over a field $k$. Then $\mathfrak{e}$ is an extension of $\mathfrak{a}$ by $\mathfrak{b}$ if $\mathfrak{a}$ is an ideal of $\mathfrak{e}$ and $\mathfrak{b}$ is isomorphic to the quotient algebra $\mathfrak{e}/\mathfrak{a}$. In this paper, by using Gr\"obner-Shirshov bases theory for associative (resp. Lie) algebras, we give complete characterizations of associative (resp. Lie) algebra extensions of $\mathfrak{a}$ by $\mathfrak{b}$, where $\mathfrak{b}$ is presented by generators and relations.

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Yuqun Chen, Jianjun Qiu. 2016-01-27. Extensions of associative and Lie algebras via Gr\"obner-Shirshov bases method. https://arxiv.org/abs/1603.01454

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