A Closed Expression for the Universal R-Matrix in a Non-Standard Quantum Double

TL;DR

This paper derives a closed-form expression for the universal R-matrix of a novel non-standard quantum double, expanding the understanding of quantum groups and their deformations.

Contribution

It provides an explicit elementary function expression for the universal R-matrix of a new quantum double example, enhancing computational and theoretical analysis.

Findings

Closed-form R-matrix expression derived

New non-standard quantum double identified

Quantum group interpreted as a deformation of a Lie algebra

Abstract

In recent papers of 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 the present paper, 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.