Rocky Mountain Journal of Mathematics

Gröbner-Shirshov bases of some Weyl groups

Eylem Güzel Karpuz, Firat Ateş, and A. Sinan Çevik

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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.

Article information

Rocky Mountain J. Math., Volume 45, Number 4 (2015), 1165-1175.

First available in Project Euclid: 2 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]

Gröbner-Shirshov basis presentation Weyl group


Karpuz, Eylem Güzel; Ateş, Firat; Çevik, A. Sinan. Gröbner-Shirshov bases of some Weyl groups. Rocky Mountain J. Math. 45 (2015), no. 4, 1165--1175. doi:10.1216/RMJ-2015-45-4-1165.

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