Abstract
A description of the commutator of a normal subcategory of the fusion category of representation Rep A of a semisimple Hopf algebra A is given. Formulae for the kernels of representations of Drinfeld doubles D(G) of finite groups G are presented. It is shown that all these kernels are normal Hopf subalgebras.
References
Bruguières A., Natale S., Exact sequences of tensor categories, Int. Math. Res. Not. IMRN, 2011, 24, 5644–5705
Burciu S., Coset decomposition for semisimple Hopf algebras, Comm. Algebra, 2009, 37(10), 3573–3585
Burciu S., Normal Hopf subalgebras of semisimple Hopf Algebras, Proc. Amer. Math. Soc., 2009, 137(12), 3969–3979
Burciu S., Categorical Hopf kernels and representations of semisimple Hopf algebras, J. Algebra, 2011, 337, 253–260
Burciu S., On coideal subalgebras of cocentral Kac algebras and a generalization of Wall’s conjecture, preprint available at http://arxiv.org/abs/1203.5491
Etingof P., Nikshych D., Ostrik V., On fusion categories, Ann. of Math., 2005, 162(2), 581–642
Gelaki S., Nikshych D., Nilpotent fusion categories, Adv. Math., 2008, 217(3), 1053–1071
Kadison L., Hopf subalgebras and tensor powers of generalized permutation modules, preprint avaliable at http://arxiv.org/abs/1210.3178
Larson R.G, Characters of Hopf algebras, J. Algebra, 1971, 17(3), 352–368
Larson R.G., Radford D.E., Finite-dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple, J. Algebra, 1988, 117(2), 267–289
Masuoka A., Semisimple Hopf algebras of dimension 2p, Comm. Algebra, 1995, 23(5), 1931–1940
Montgomery S., Hopf algebras and their actions on rings, In: CBMS Reg. Conf. Ser. Math., 82, American Mathematical Society, Providence, 1993
Müger M., On the structure of modular categories, Proc. London Math. Soc., 2003, 87(2), 291–308
Naidu D., Nikshych D., Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups, Comm. Math. Phys., 2008, 279(3), 845–872
Naidu D., Nikshych D., Witherspoon S., Fusion subcategories of representation categories of twisted quantum doubles of finite groups, Int. Math. Res. Not. IMRN, 2009, 22, 4183–4219
Nichols W.D., Richmond M.B., The Grothendieck algebra of a Hopf algebra. I, Comm. Algebra, 1988, 26(4), 1081–1095
Nichols W.D., Richmond M.B., The Grothendieck group of a Hopf algebra, J. Pure Appl. Algebra, 1996, 106(3), 297–306
Passman D.S., Quinn D., Burnside’s theorem for Hopf algebras, Proc. Amer. Math. Soc., 1995, 123(2), 327–333
Sommerhäuser Y., On Kaplansky’s fifth conjecture, J. Algebra, 1998, 204(1), 202–224
Zhu Y., Hopf algebras of prime dimension, Int. Math. Res. Not. IMRN, 1994, 1, 53–59
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Burciu, S. Kernels of representations of Drinfeld doubles of finite groups. centr.eur.j.math. 11, 1900–1913 (2013). https://doi.org/10.2478/s11533-013-0298-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-013-0298-5