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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 230–237 (Mi smj2855)  

Gröbner–Shirshov bases for some Lie algebras

Yu. Chena, Y. Lib, Q. Tanga

a 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.

Funding Agency Grant Number
National Natural Science Foundation of China 11171118
11571121
11401246
11426112
11501237
Natural Science Foundation of Guangdong Province 2014A030310087
2016A030310099
Foundation for Distinguished Young Teachers in Higher Education of Guangdong YQ2015155
Huizhou University C513.0210
C513.0209
The authors were supported by the NNSF of China (11171118; 11571121). The second author was supported by the NNSF of China (11401246; 11426112; 11501237), the NSF of the Guangdong Province (2014A030310087; 2016A030310099), the Foundation for Distinguished Young Teachers in Higher Education of Guangdong (Grant YQ2015155), and the Research Fund for the Doctoral Program of Huizhou University (C513.0210; C513.0209).


DOI: https://doi.org/10.17377/smzh.2017.58.122

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

Bibliographic databases:

Document Type: Article
UDC: 512.554
MSC: 17B01, 16S15, 3P10, 20M05, 03D15
Received: 13.05.2013

Citation: Yu. Chen, Y. Li, Q. Tang, “Gröbner–Shirshov bases for some Lie algebras”, Sibirsk. Mat. Zh., 58:1 (2017), 230–237; Siberian Math. J., 58:1 (2017), 176–182

Citation in format AMSBIB
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\pages 230--237
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\pages 176--182
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