Two-parameter nonstandard deformation of 2x2 matrices

Abstract

We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup $G{L}_{p,q}(1|1)$ by a transformation.

10 pages

References in corpus (2)

• $h$-Deformation as a Contraction of $q$-Deformation
• The quantum de Rham complexes associated with $S{L}_h(2)$