Groebner-Shirshov basis for the braid semigroup

TL;DR

This paper introduces a Groebner-Shirshov basis for the braid semigroup, providing a new algorithm to solve the word problem for braid groups, which enhances computational approaches in algebra.

Contribution

The paper presents the first Groebner-Shirshov basis for the braid semigroup, enabling more efficient solutions to the word problem in braid theory.

Findings

Developed a Groebner-Shirshov basis for $B^+_{n+1}$

Provided a new algorithm for the word problem

Improved computational methods in braid group theory

Abstract

We found Groebner-Shirshov basis for the braid semigroup $B^+_{n+1}$. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group.