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

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

2008-06-06

arxiv.org/abs/0806.1123v1

Mathematics

Group Theory

Scientific paper

In this paper, we obtain Groebner-Shirshov (non-commutative Gr\"obner) bases
for the braid groups in the Birman-Ko-Lee generators enriched by new ``Garside
word" $\delta$. 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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