Kernels of representations of Drinfeld doubles of finite groups

• Autorzy: Sebastian Burciu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Normal fusion subcategories; Drinfeld doubles of finite groups; Fusion subcategories; Kernels of representations

Kategorie tematyczne

• 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 11
• Strony: 1900-1913

Daty

wydano

2013-11-01

online

2013-08-23

Twórcy

autor

Sebastian Burciu

Bibliografia

• [1] Bruguières A., Natale S., Exact sequences of tensor categories, Int. Math. Res. Not. IMRN, 2011, 24, 5644–5705
• [2] Burciu S., Coset decomposition for semisimple Hopf algebras, Comm. Algebra, 2009, 37(10), 3573–3585 http://dx.doi.org/10.1080/00927870902828496
• [3] Burciu S., Normal Hopf subalgebras of semisimple Hopf Algebras, Proc. Amer. Math. Soc., 2009, 137(12), 3969–3979 http://dx.doi.org/10.1090/S0002-9939-09-09965-1
• [4] Burciu S., Categorical Hopf kernels and representations of semisimple Hopf algebras, J. Algebra, 2011, 337, 253–260 http://dx.doi.org/10.1016/j.jalgebra.2011.04.006
• [5] 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
• [6] Etingof P., Nikshych D., Ostrik V., On fusion categories, Ann. of Math., 2005, 162(2), 581–642 http://dx.doi.org/10.4007/annals.2005.162.581
• [7] Gelaki S., Nikshych D., Nilpotent fusion categories, Adv. Math., 2008, 217(3), 1053–1071 http://dx.doi.org/10.1016/j.aim.2007.08.001
• [8] Kadison L., Hopf subalgebras and tensor powers of generalized permutation modules, preprint avaliable at http://arxiv.org/abs/1210.3178
• [9] Larson R.G, Characters of Hopf algebras, J. Algebra, 1971, 17(3), 352–368 http://dx.doi.org/10.1016/0021-8693(71)90018-4
• [10] Larson R.G., Radford D.E., Finite-dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple, J. Algebra, 1988, 117(2), 267–289 http://dx.doi.org/10.1016/0021-8693(88)90107-X
• [11] Masuoka A., Semisimple Hopf algebras of dimension 2p, Comm. Algebra, 1995, 23(5), 1931–1940 http://dx.doi.org/10.1080/00927879508825319
• [12] Montgomery S., Hopf algebras and their actions on rings, In: CBMS Reg. Conf. Ser. Math., 82, American Mathematical Society, Providence, 1993
• [13] Müger M., On the structure of modular categories, Proc. London Math. Soc., 2003, 87(2), 291–308 http://dx.doi.org/10.1112/S0024611503014187
• [14] 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 http://dx.doi.org/10.1007/s00220-008-0441-5
• [15] 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
• [16] Nichols W.D., Richmond M.B., The Grothendieck algebra of a Hopf algebra. I, Comm. Algebra, 1988, 26(4), 1081–1095 http://dx.doi.org/10.1080/00927879808826185
• [17] Nichols W.D., Richmond M.B., The Grothendieck group of a Hopf algebra, J. Pure Appl. Algebra, 1996, 106(3), 297–306 http://dx.doi.org/10.1016/0022-4049(95)00023-2
• [18] Passman D.S., Quinn D., Burnside’s theorem for Hopf algebras, Proc. Amer. Math. Soc., 1995, 123(2), 327–333
• [19] Sommerhäuser Y., On Kaplansky’s fifth conjecture, J. Algebra, 1998, 204(1), 202–224 http://dx.doi.org/10.1006/jabr.1997.7337
• [20] Zhu Y., Hopf algebras of prime dimension, Int. Math. Res. Not. IMRN, 1994, 1, 53–59 http://dx.doi.org/10.1155/S1073792894000073

Identyfikatory

DOI

10.2478/s11533-013-0298-5