Makale detayı · 2015 · article
Gröbner Shirshov Bases of Some Weyl Groups
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- YÖKSİSYÖKSİS makale kaydı
- YÖKSİS dergi adıRocky Mountain Journal of Mathematics
- Katalog eşleşmesi (ISSN)Rocky Mountain Journal of Mathematics
- OpenAlexOpenAlex zenginleştirmesi (özet, atıf, konular)
Özet
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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