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2015 Gröbner-Shirshov bases of some Weyl groups
Eylem Güzel Karpuz, Firat Ateş, A. Sinan Çevik
Rocky Mountain J. Math. 45(4): 1165-1175 (2015). DOI: 10.1216/RMJ-2015-45-4-1165

Abstract

In this paper, we obtain Gr\"{o}bner-Shirshov (non-commutative) bases for the $n$-extended affine Weyl group $\widetilde{W}$ of type $A_1$, elliptic Weyl groups of types $A_{1}^{(1,1)}$, $A_{1}^{(1,1)^{*}}$ and the $2$-extended affine Weyl group of type $A_{2}^{(1,1)}$ with a generator system of a $2$-toroidal sense. It gives a new algorithm for getting normal forms of elements of these groups and hence a new algorithm for solving the word problem in these groups.

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Eylem Güzel Karpuz. Firat Ateş. A. Sinan Çevik. "Gröbner-Shirshov bases of some Weyl groups." Rocky Mountain J. Math. 45 (4) 1165 - 1175, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1165

Information

Published: 2015
First available in Project Euclid: 2 November 2015

zbMATH: 0895.16020
MathSciNet: MR3418188
Digital Object Identifier: 10.1216/RMJ-2015-45-4-1165

Subjects:
Primary: 13P10
Secondary: 20F55

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 4 • 2015
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