Gröbner-Shirshov bases of some Weyl groups (Q888111)

The main goal of this paper is to obtain Gröbner-Shirshov bases for the \(n\)-extended affine Weyl group of type \(A_1\), elliptic Weyl groups of types \(A^{(1,1)}_{1}\), \(A^{(1,1)^*}_{1}\) and \(2\)-extended affine Weyl group of type \(A^{(1,1)}_{2}\) with a generator system of a \(2\)-toroidal sense. These Göbner-Shirshov bases give an opportunity to get normal forms of the elements of these groups.