This article is cited in 2 papers

Gröbner–Shirshov bases for some Lie algebras

Yu. Chen^a, Y. Li^b, Q. Tang<sup>a

a</sup> School of Mathematical Sciences, South China Normal University, Guangzhou, P. R. China
^b Department of Mathematics, Huizhou University, Huizhou, P. R. China

Abstract: We give Gröbner–Shirshov bases for the Drinfeld–Kohno Lie algebra $\mathbf L_n$ in [1] and the Kukin Lie algebra $A_P$ in [2], where $P$ is a semigroup. By way of application, we show that $\mathbf L_n$ is free as a $\mathbb Z$-module and exhibit a $\mathbb Z$-basis for $\mathbf L_n$. We give another proof of the Kukin Theorem: If $P$ has the undecidable word problem then so is $A_P$.

Keywords: Gröbner–Shirshov basis, Lie algebra, Drinfeld–Kohno Lie algebra, word problem, semigroup.

UDC: 512.554

MSC: 17B01, 16S15, 3P10, 20M05, 03D15

Received: 13.05.2013

DOI: 10.17377/smzh.2017.58.122

 English version: Siberian Mathematical Journal, 2017, 58:1, 176–182

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