Gröbner-Shirshov Basis for Complex Reflection Group

Year 2019, Volume: 7 Issue: 1, 79 - 90, 15.04.2019

Eylem Güzel Karpuz , Nurten Urlu Özalan , Ahmet Sinan Çevik

Abstract

The aim of this paper is to obtain a (non-commutative) Gröbner-Shirshov basis for the braid group associated with the complex reflection group $G_{24}$. This gives us an opportunity to get normal forms of the elements of group $G_{24}$, which represent a new and effective algorithm to solve the word problem over it.

Keywords

Braid group, Gröbner-Shirshov basis, presentation, word problem

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