The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra

TL;DR

This paper constructs a twist operator for the Jordanian quasi-Hopf algebra U_{h;y}(sl(2)) using a contraction method, leading to a universal R-matrix satisfying a Gervais-Neveu-Felder equation, with implications for the dynamical Yang-Baxter equation.

Contribution

It introduces a new twist operator satisfying a shifted cocycle condition for the Jordanian quasi-Hopf algebra U_{h;y}(sl(2)).

Findings

Derived a universal R-matrix obeying the Gervais-Neveu-Felder equation.

Connected the algebraic structure to the dynamical Yang-Baxter equation.

Provided a contraction-based construction method for the twist operator.

Abstract

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra. The corresponding universal ${\cal R}_{h}(y)$ matrix obeys a Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a class of representations, the dynamical Yang-Baxter equation may be expressed as a compatibility condition for the algebra of the Lax operators.