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math.RAApr 8, 2008
25
citations (OpenAlex)
authors
  • L. A. Bokut
  • Yuqun Chen
institutions
  • Novosibirsk State University
  • Russian Academy of Sciences
  • Sobolev Institute of Mathematics
  • South China Normal University
arXiv abstractPDF
paper

Groebner-Shirshov Bases for Lie Algebras: after A. I. Shirshov

arXiv:0804.1254

Abstract

In this paper, we review Shirshov's method for free Lie algebras invented by him in 1962 which is now called the Groebner-Shirshov bases theory.

18 pages

Cited by in corpus (11)

  • Gröbner-Shirshov bases for Lie algebras over a commutative algebra
  • Lyndon-Shirshov basis and anti-commutative algebras
  • HNN-extension of Lie superalgebras
  • Gröbner-Shirshov bases and PBW theorems
  • Gröbner-Shirshov bases and embeddings of algebras
  • Lyndon words for Artin-Schelter regular algebras
  • Gröbner-Shirshov bases for categories
  • Bases for partially commutative Lie algebras
  • Tangent complexes and the Diamond Lemma
  • Filtrations and Distortion in Infinite-Dimensional Algebras
  • Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures
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