Markov and Artin Normal Form Theorem for Braid Groups∗

∗Dedicated to 80th birthday of Boris Isaakovich Plotkin.

Abstract

In this article, we will present the results of Artin–Markov on braid groups by using the Gröbner–Shirshov basis. As a consequence, we can reobtain the normal form of Artin–Markov–Ivanovsky as an easy corollary.

Key Words:

• Braid group
• Diamond lemma
• Gröbner–Shirshov basis
• Normal form
• Rewriting system

Mathematics Subject Classification:

• Primary 20F36
• Secondary 16S15

ACKNOWLEDGMENT

Bokut is supported in part by the Russia's Fund for Fundamental Research and the Leading Scientific Schools Fund. The research of the third author is partially supported by a RGC grant (CUHK) #2060297 (05-07).

Notes

Communicated by A. I. Zelmanov.

∗Dedicated to 80th birthday of Boris Isaakovich Plotkin.