Representations and Conjugacy Classes of Semisimple Quasitriangular Hopf Algebras

TL;DR

This paper provides two general formulas for M"uger centralizers in the representation categories of semisimple quasitriangular Hopf algebras, linking the Drinfeld map and conjugacy classes, extending previous results.

Contribution

It introduces two new general formulas for M"uger centralizers, connecting the Drinfeld map and conjugacy classes in semisimple quasitriangular Hopf algebras.

Findings

Formulas expressed via the Drinfeld map.

Formulas expressed via conjugacy classes.

Extensions to factorizable Hopf algebras.

Abstract

In this paper we give two general formulae for the M\"uger centralizers in the category of representations of a semisimple quasitriangular Hopf algebra. The first formula is given in the terms of the Drinfeld map associated to the quasitriangular Hopf algebra. The second formula for the M\"uger centralizer is given in the terms of the conjugacy classes introduced by Cohen and Westreich in [J. Algebra 283 (2005), 42-62]. In the case of a factorizable Hopf algebra these formulae extend some particular cases obtained by the author in [Math. Z. 279 (2015), 227-240].