Fusion of q-tensor operators: quasi-Hopf-algebraic point of view

TL;DR

This paper explores the fusion of tensor operators in quantum Lie algebras using R-matrix methods, focusing on the quantum WZNW model and constructing a quasi-Hopf algebraic twisting element.

Contribution

It introduces a new approach to tensor operator fusion via the construction of a twisting element in the quasi-Hopf algebra framework.

Findings

Constructed the twisting element F(p) for quantum Lie algebras.

Applied the method to the fundamental representation of U_q(sl(2)).

Provided calculations illustrating the fusion process.

Abstract

Tensor operators associated with a given quantum Lie algebra admit a natural description in the R-matrix language. Here we employ the R-matrix approach to discuss the problem of fusion of tensor operators. The most interesting case is provided by the quantum WZNW model, where, by construction, we deal with sets of linearly independent tensor operators. In this case the fusion problem is equivalent to construction of an analogue F(p) of the twisting element F which is employed in Drinfeld's description of quasi-Hopf algebras. We discuss the construction of the twisting element F(p) in a general situation and give illustrating calculations for the case of the fundamental representation of U_q(sl(2)).