• [1] Proceedings of the International Congress of Mathematicians. Vol. I, II, Mathematical Society of Japan, Tokyo; Springer-Verlag, Tokyo, 1991. Held in Kyoto, August 21–29, 1990; Edited by Ichirô Satake. MR 1159197
• [2] John C. Baez and James Dolan, Categorification, Higher category theory (Evanston, IL, 1997) Contemp. Math., vol. 230, Amer. Math. Soc., Providence, RI, 1998, pp. 1–36. MR 1664990, https://doi.org/10.1090/conm/230/03336
• [3] Bojko Bakalov and Alexander Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series, vol. 21, American Mathematical Society, Providence, RI, 2001. MR 1797619
• [4] B. Bartlett, C. L. Douglas, C. J. Schommer-Pries, and J. Vicary, Modular categories as representations of the -dimensional bordism -category, ArXiv e-prints (2015).
• [5] Paul Bruillard, Siu-Hung Ng, Eric C. Rowell, and Zhenghan Wang, Rank-finiteness for modular categories, J. Amer. Math. Soc. 29 (2016), no. 3, 857–881. MR 3486174, https://doi.org/10.1090/S0894-0347-2015-00842-6
• [6] Pavel Etingof and Shlomo Gelaki, Some properties of finite-dimensional semisimple Hopf algebras, Math. Res. Lett. 5 (1998), no. 1-2, 191–197. MR 1617921, https://doi.org/10.4310/MRL.1998.v5.n2.a5
• [7] Pavel Etingof, Dmitri Nikshych, and Viktor Ostrik, On fusion categories, Ann. of Math. (2) 162 (2005), no. 2, 581–642. MR 2183279, https://doi.org/10.4007/annals.2005.162.581
• [8] V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335–388. MR 908150, https://doi.org/10.2307/1971403
• [9] Vaughan F. R. Jones, Scott Morrison, and Noah Snyder, The classification of subfactors of index at most 5, Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 2, 277–327. MR 3166042, https://doi.org/10.1090/S0273-0979-2013-01442-3
• [10] André Joyal and Ross Street, Braided tensor categories, Adv. Math. 102 (1993), no. 1, 20–78. MR 1250465, https://doi.org/10.1006/aima.1993.1055
• [11] M. M. Kapranov and V. A. Voevodsky, 2-categories and Zamolodchikov tetrahedra equations, Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991) Proc. Sympos. Pure Math., vol. 56, Amer. Math. Soc., Providence, RI, 1994, pp. 177–259. MR 1278735
• [12] Alexander Kirillov Jr. and Viktor Ostrik, On a 𝑞-analogue of the McKay correspondence and the ADE classification of 𝔰𝔩₂ conformal field theories, Adv. Math. 171 (2002), no. 2, 183–227. MR 1936496, https://doi.org/10.1006/aima.2002.2072
• [13] S. Mac Lane, The PNAS way back then, Proceedings of the National Academy of Sciences 94 (1997), no. 12, 5983-5985.
• [14] Gregory Moore and Nathan Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123 (1989), no. 2, 177–254. MR 1002038
• [15] Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, Non-abelian anyons and topological quantum computation, Rev. Modern Phys. 80 (2008), no. 3, 1083–1159. MR 2443722, https://doi.org/10.1103/RevModPhys.80.1083
• [16] Adrian Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Operator algebras and applications, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 136, Cambridge Univ. Press, Cambridge, 1988, pp. 119–172. MR 996454
• [17] B. Pareigis, Non-additive ring and module theory. II. \cal𝐶-categories, \cal𝐶-functors and \cal𝐶-morphisms, Publ. Math. Debrecen 24 (1977), no. 3-4, 351–361. MR 498792
• [18] N. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597. MR 1091619, https://doi.org/10.1007/BF01239527
• [19] Vladimir Turaev and Hans Wenzl, Semisimple and modular categories from link invariants, Math. Ann. 309 (1997), no. 3, 411–461. MR 1474200, https://doi.org/10.1007/s002080050120
• [20] Vladimir G. Turaev, Modular categories and 3-manifold invariants, Internat. J. Modern Phys. B 6 (1992), no. 11-12, 1807–1824. Topological and quantum group methods in field theory and condensed matter physics. MR 1186845, https://doi.org/10.1142/S0217979292000876
• [21] Hans Wenzl, 𝐶* tensor categories from quantum groups, J. Amer. Math. Soc. 11 (1998), no. 2, 261–282. MR 1470857, https://doi.org/10.1090/S0894-0347-98-00253-7
• [22] Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. MR 990772

References

[1]

Proceedings of the International Congress of Mathematicians. Vol. I, II: Edited by I. Satake, Mathematical Society of Japan, Tokyo; Springer-Verlag, Tokyo, 1991. Held in Kyoto, August 21-29, 1990. MR 1159197

[2]

John C. Baez and James Dolan, Categorification, Higher category theory (Evanston, IL, 1997) Contemp. Math., vol. 230, Amer. Math. Soc., Providence, RI, 1998, pp. 1-36. MR 1664990, https://doi.org/10.1090/conm/230/03336

[3]

Bojko Bakalov and Alexander Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series, vol. 21, American Mathematical Society, Providence, RI, 2001. MR 1797619

[4]

B. Bartlett, C. L. Douglas, C. J. Schommer-Pries, and J. Vicary, Modular categories as representations of the -dimensional bordism -category, ArXiv e-prints (2015).

[5]

Paul Bruillard, Siu-Hung Ng, Eric C. Rowell, and Zhenghan Wang, Rank-finiteness for modular categories, J. Amer. Math. Soc. 29 (2016), no. 3, 857-881. MR 3486174, https://doi.org/10.1090/jams/842

[6]

Pavel Etingof and Shlomo Gelaki, Some properties of finite-dimensional semisimple Hopf algebras, Math. Res. Lett. 5 (1998), no. 1-2, 191-197. MR 1617921, https://doi.org/10.4310/MRL.1998.v5.n2.a5

[7]

Pavel Etingof, Dmitri Nikshych, and Viktor Ostrik, On fusion categories, Ann. of Math. (2) 162 (2005), no. 2, 581-642. MR 2183279, https://doi.org/10.4007/annals.2005.162.581

[8]

V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335-388. MR 0908150, https://doi.org/10.2307/1971403

[9]

Vaughan F. R. Jones, Scott Morrison, and Noah Snyder, The classification of subfactors of index at most , Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 2, 277-327. MR 3166042, https://doi.org/10.1090/S0273-0979-2013-01442-3

[10]

André Joyal and Ross Street, Braided tensor categories, Adv. Math. 102 (1993), no. 1, 20-78. MR 1250465, https://doi.org/10.1006/aima.1993.1055

[11]

M. M. Kapranov and V. A. Voevodsky, -categories and Zamolodchikov tetrahedra equations, Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991) Proc. Sympos. Pure Math., vol. 56, Amer. Math. Soc., Providence, RI, 1994, pp. 177-259. MR 1278735

[12]

Alexander Kirillov Jr. and Viktor Ostrik, On a -analogue of the McKay correspondence and the ADE classification of conformal field theories, Adv. Math. 171 (2002), no. 2, 183-227. MR 1936496, https://doi.org/10.1006/aima.2002.2072

[13]

S. Mac Lane, The PNAS way back then, Proceedings of the National Academy of Sciences 94 (1997), no. 12, 5983-5985.

[14]

Gregory Moore and Nathan Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123 (1989), no. 2, 177-254. MR 1002038

[15]

Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, Non-abelian anyons and topological quantum computation, Rev. Modern Phys. 80 (2008), no. 3, 1083-1159. MR 2443722, https://doi.org/10.1103/RevModPhys.80.1083

[16]

Adrian Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Operator algebras and applications, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 136, Cambridge Univ. Press, Cambridge, 1988, pp. 119-172. MR 0996454

[17]

B. Pareigis, Non- additive ring and module theory. II. -categories, -functors and -morphisms, Publ. Math. Debrecen 24 (1977), no. 3-4, 351-361. MR 0498792

[18]

N. Reshetikhin and V. G. Turaev, Invariants of -manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547-597. MR 1091619, https://doi.org/10.1007/BF01239527

[19]

Vladimir Turaev and Hans Wenzl, Semisimple and modular categories from link invariants, Math. Ann. 309 (1997), no. 3, 411-461. MR 1474200, https://doi.org/10.1007/s002080050120

[20]

Vladimir G. Turaev, Modular categories and -manifold invariants: Topological and quantum group methods in field theory and condensed matter physics, Internat. J. Modern Phys. B 6 (1992), no. 11-12, 1807-1824. MR 1186845, https://doi.org/10.1142/S0217979292000876

[21]

Hans Wenzl, tensor categories from quantum groups, J. Amer. Math. Soc. 11 (1998), no. 2, 261-282. MR 1470857, https://doi.org/10.1090/S0894-0347-98-00253-7

[22]

Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351-399. MR 0990772