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

Yıl 2024, Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 86 - 101, 29.12.2024

Uğur Ustaoğlu

https://doi.org/10.33773/jum.1562793

Öz

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.

Anahtar Kelimeler

Gr\"{o}bner-Shirshov Bases , coxeter groups , normal forms

Kaynakça

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