On Up,q(gl(2)) and a (p,q)-Virasoro algebra

Abstract

The quantum algebra Up,q(gl(2)), with two independent deformation parameters (p, q), is studied and, in particular, its universal R-matrix is constructed using Reshetikhin's method. A contraction procedure then leads to the (p, q)-deformed Heisenberg algebra Up, q(h(1)) and its universal R-matrix. Using a Sugawara construction employing an infinite number of copies of these Heisenberg modes, a (p, q)-deformed Virasoro algebra is obtained. The closure property of the (p, q)-Virasoro algebra necessitates two parameters ( alpha , beta ) for the generators (Lm( alpha , beta )). While the parameter alpha may be taken as an integer, the parameter beta is continuous on a complex path and imparts an integral equation structure to the (p, q)-deformed Virasoro algebra.