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2013 | 11 | 11 | 1900-1913
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Kernels of representations of Drinfeld doubles of finite groups

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EN
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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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
11
Strony
1900-1913
Opis fizyczny
Daty
wydano
2013-11-01
online
2013-08-23
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
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0298-5
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