Gröbner-Shirshov bases for some Lie algebras

Abstract

We give Gröbner-Shirshov bases for Drinfeld-Kohno Lie algebra ${\text{L}}_n$ 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 ${\text{L}}_n$ is free and a $\mathbb{Z}$-basis of ${\text{L}}_n$ 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.

10 pages. arXiv admin note: substantial text overlap with arXiv:1303.5366

References in corpus (4)

• Groebner-Shirshov Bases: Some New Results
• Gröbner-Shirshov bases for Lie algebras over a commutative algebra
• Lyndon-Shirshov basis and anti-commutative algebras
• Gröbner-Shirshov bases for semirings

Cited by in corpus (2)

• Gröbner-Shirshov bases for semirings
• Gröbner-Shirshov bases and PBW theorems