Representations and Conjugacy Classes of Semisimple Quasitriangular Hopf Algebras

Abstract

In this paper, we give two general formulae for the Müger centralizers in the category of representations of a semisimple quasitriangular Hopf algebra. The first formula is given in terms of the Drinfeld map associated with the quasitriangular Hopf algebra. The second formula for the Müger centralizer is given in 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].