Anti-commutative Groebner-Shirshov basis of a free Lie algebra
Rings and Algebras
2015-05-13 v1
Abstract
One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and then to check that the product yields the Lie identities (Marshall Hall, 1950). Here we suggest another way using the Composition-Diamond lemma for free anti-commutative (non-associative) algebras (A.I. Shirshov, 1962).
Keywords
Cite
@article{arxiv.0804.0914,
title = {Anti-commutative Groebner-Shirshov basis of a free Lie algebra},
author = {L. A. Bokut and Yuqun Chen and Yu Li},
journal= {arXiv preprint arXiv:0804.0914},
year = {2015}
}