Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 039, 20 pages      arXiv:1709.02176      https://doi.org/10.3842/SIGMA.2020.039

Representations and Conjugacy Classes of Semisimple Quasitriangular Hopf Algebras

Sebastian Burciu
Institute of Mathematics ''Simion Stoilow'' of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania

Received September 16, 2019, in final form April 27, 2020; Published online May 06, 2020

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 the terms of the Drinfeld map associated to the quasitriangular Hopf algebra. The second formula for the Müger 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].

Key words: quasi-triangular Hopf algebras; centralizers; braided fusion categories; normal coideal subalgebras.

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