Volume 13, issue 3 (2013)

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Faithful simple objects, orders and gradings of fusion categories

Sonia Natale

Algebraic & Geometric Topology 13 (2013) 1489–1511
Bibliography
1 H H Andersen, J Paradowski, Fusion categories arising from semisimple Lie algebras, Comm. Math. Phys. 169 (1995) 563 MR1328736
2 B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series 21, American Mathematical Society (2001) MR1797619
3 J Bichon, S Natale, Hopf algebra deformations of binary polyhedral groups, Transform. Groups 16 (2011) 339 MR2806496
4 P Bonderson, Non-abelian anyons and interfermetry, PhD thesis, California Institute of Technology (2007)
5 A Bruguières, Catégories prémodulaires, modularisations et invariants des variétés de dimension 3, Math. Ann. 316 (2000) 215 MR1741269
6 A Bruguières, S Natale, Exact sequences of tensor categories, Int. Math. Res. Not. 2011 (2011) 5644 MR2863377
7 S Burciu, Kernels of representations and coideal subalgebras of Hopf algebras, Glasg. Math. J. 54 (2012) 107 MR2862388
8 V Drinfeld, S Gelaki, D Nikshych, V Ostrik, Group-theoretical properties of nilpotent modular categories arXiv:0704.0195
9 V Drinfeld, S Gelaki, D Nikshych, V Ostrik, On braided fusion categories, I, Selecta Math. 16 (2010) 1 MR2609644
10 P Etingof, D Nikshych, V Ostrik, On fusion categories, Ann. of Math. 162 (2005) 581 MR2183279
11 P Etingof, D Nikshych, V Ostrik, Fusion categories and homotopy theory, Quantum Topol. 1 (2010) 209 MR2677836
12 P Etingof, D Nikshych, V Ostrik, Weakly group-theoretical and solvable fusion categories, Adv. Math. 226 (2011) 176 MR2735754
13 P Etingof, V Ostrik, Module categories over representations of $\mathrm{SL}_q(2)$ and graphs, Math. Res. Lett. 11 (2004) 103 MR2046203
14 S Gelaki, D Nikshych, Nilpotent fusion categories, Adv. Math. 217 (2008) 1053 MR2383894
15 S m Hong, E Rowell, On the classification of the Grothendieck rings of non-self-dual modular categories, J. Algebra 324 (2010) 1000 MR2659210
16 I M Isaacs, Character theory of finite groups, Pure and Applied Mathematics 69, Academic Press [Harcourt Brace Jovanovich Publishers] (1976) MR0460423
17 Y Kashina, Y Sommerhäuser, Y Zhu, On higher Frobenius–Schur indicators, Mem. Amer. Math. Soc. 181 (2006) MR2213320
18 J Liptrap, Generalized Tambara–Yamagami categories, to appear in Journal of Algebra (2010) arXiv:1002.3166v2
19 M Müger, Galois theory for braided tensor categories and the modular closure, Adv. Math. 150 (2000) 151 MR1749250
20 M Müger, On the structure of modular categories, Proc. London Math. Soc. 87 (2003) 291 MR1990929
21 S Natale, Hopf algebra extensions of group algebras and Tambara–Yamagami categories, Algebr. Represent. Theory 13 (2010) 673 MR2736029
22 S H Ng, P Schauenburg, Frobenius–Schur indicators and exponents of spherical categories, Adv. Math. 211 (2007) 34 MR2313527
23 V Ostrik, Fusion categories of rank 2, Math. Res. Lett. 10 (2003) 177 MR1981895
24 F Quinn, Group categories and their field theories, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2 (1999) 407 MR1734419
25 E Rowell, R Stong, Z Wang, On classification of modular tensor categories, Comm. Math. Phys. 292 (2009) 343 MR2544735
26 J Siehler, Braided near-group categories arXiv:math/0011037
27 J Siehler, Near-group categories, Algebr. Geom. Topol. 3 (2003) 719 MR1997336
28 D Tambara, S Yamagami, Tensor categories with fusion rules of self-duality for finite abelian groups, J. Algebra 209 (1998) 692 MR1659954
29 J Thornton, On braided near-group categories arXiv:1102.4640v1
30 V G Turaev, Quantum invariants of knots and 3-manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673