GRÖBNER-SHIRSHOV BASES AND NORMAL FORMS FOR THE INFINITE COXETER GROUPS OF TYPES $\\\\widetilde{B}_{n}$ and $\\\\widetilde{D}_n$

Authors : Uğur Ustaoğlu

Pages : 86-101

Doi:10.33773/jum.1562793

View : 39 | Download : 47

Publication Date : 2024-12-29

Article Type : Review Paper

Abstract :In this paper, we will investigate the infinite Coxeter groups $\\\\widetilde{B}_n$ and $\\\\widetilde{D}_n$. Their Gr\\\\\\\"{o}bner-Shirshov bases and classifications of normal forms are achieved by leveraging results from the infinite Coxeter groups of types $\\\\widetilde{C}_n$. Additionally, a new algorithm is presented for obtaining normal forms of elements within these groups.
Keywords : Gr\\\"{o}bner-Shirshov Bases, coxeter groups, normal forms