A CLOSED EXPRESSION FOR THE UNIVERSAL ℛ-MATRIX IN A NON-STANDARD QUANTUM DOUBLE

Abstract

In recent papers by the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In this letter, a closed expression (in terms of elementary functions) for the corresponding universal ℛ-matrix is obtained. In reduced form, when the number of generators becomes two instead of four, this quantum group can be interpreted as a deformation of the Lie algebra [x, h]=2h in the context of Drinfeld’s quantization program.