Groebner-Shirshov basis for the braid group in the Birman-Ko-Lee-Garside generators

2008/06/06 by L. A. Bokut, Bokut, L. A.
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.0806.1123

arxiv created 2008/06/06 · arxiv updated 2009/12/01

Abstract

In this paper, we obtain Groebner-Shirshov (non-commutative Gröbner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new ``Garside word" δ. It gives a new algorithm for getting the Birman-Ko-Lee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.

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