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

2008/06/06 by L. A. Bokut, Bokut, L. A.
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.0806.1125

arxiv created 2008/06/06 · openalex publication_date 2008/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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