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arXiv · 1305.4546

Gr\"obner-Shirshov bases for some Lie algebras

Yuqun Chen·Yu Li·Qingyan Tang
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Abstract

We give Gr\"obner-Shirshov bases for Drinfeld-Kohno Lie algebra $\textbf{L}_{n}$ in \cite{[Et]} and Kukin Lie algebra $A_P$ in \cite{Kukin}, where $P$ is a semigroup. As applications, we show that as $\mathbb{Z}$-module $\textbf{L}_{n}$ is free and a $\mathbb{Z}$-basis of $\textbf{L}_{n}$ is given. We give another proof of Kukin Theorem: if semigroup $P$ has the undecidable word problem then the Lie algebra $A_P$ has the same property.

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Yuqun Chen, Yu Li, Qingyan Tang. 2013-05-15. Gr\"obner-Shirshov bases for some Lie algebras. https://arxiv.org/abs/1305.4546

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