Volume 13, issue 3 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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