On universal solution to reflection equation

TL;DR

This paper introduces a universal solution to the reflection equation within the framework of quasitriangular Hopf algebras, linking braided groups, Drinfeld twists, and fusion procedures for RE-matrices.

Contribution

It provides a new universal solution to the reflection equation and connects braided group structures with twisted tensor powers of Hopf algebras.

Findings

Universal RE-solution expressed via twisted tensor powers

Fusion prescription for RE-matrices derived

Braided bialgebra structure characterized by Drinfeld twists

Abstract

For a given quasitriangular Hopf algebra $\Ha$ we study relations between the braided group $\tilde \Ha^*$ and Drinfeld's twist. We show that the braided bialgebra structure of $\tilde \Ha^*$ is naturally described by means of twisted tensor powers of $\Ha$ and their module algebras. We introduce universal solution to the reflection equation (RE) and deduce a fusion prescription for RE-matrices