Groebner-Shirshov basis for the braid group in the Artin-Garside generators

L. A. Bokut

Groebner-Shirshov basis for the braid group in the Artin-Garside generators

Group Theory 2008-06-09 v1 Combinatorics

Authors: L. A. Bokut

Abstract

In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ in the Artin--Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup $B^+{n+1}$ is the subsemigroup in $B_{n+1}$ .

Keywords

Groebner-Shirshov basis braid group Artin-Garside generators Garside normal form braid semigroup

Cite

@article{arxiv.0806.1125,
  title  = {Groebner-Shirshov basis for the braid group in the Artin-Garside generators},
  author = {L. A. Bokut},
  journal= {arXiv preprint arXiv:0806.1125},
  year   = {2008}
}

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