Simple current auto-equivalences of modular tensor categories

Edie-Michell, Cain

doi:10.1090/proc/14795

Simple current auto-equivalences of modular tensor categories
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Proc. Amer. Math. Soc. 148 (2020), 1415-1428 Request permission

Abstract:

In this short note we investigate the process of using invertible objects to construct auto-equivalences of modular tensor categories. We derive conditions on the invertible object for the resulting auto-equivalence to be either monoidal, braided, or pivotal. We also discuss the composition of these auto-equivalences constructed from invertible objects. To demonstrate the practicality of this construction, we construct auto-equivalences of several real-world examples of modular tensor categories.

References

Denis Bernard, String characters from Kac-Moody automorphisms, Nuclear Phys. B 288 (1987), no. 3-4, 628–648. MR 892062, DOI 10.1016/0550-3213(87)90231-8
Shawn X. Cui, César Galindo, Julia Yael Plavnik, and Zhenghan Wang, On gauging symmetry of modular categories, Comm. Math. Phys. 348 (2016), no. 3, 1043–1064. MR 3555361, DOI 10.1007/s00220-016-2633-8
Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik, On braided fusion categories. I, Selecta Math. (N.S.) 16 (2010), no. 1, 1–119. MR 2609644, DOI 10.1007/s00029-010-0017-z
Cain Edie-Michell, Equivalences of graded categories, arXiv:1711.00645 (2017).
Terry Gannon, The automorphisms of affine fusion rings, Adv. Math. 165 (2002), no. 2, 165–193. MR 1887583, DOI 10.1006/aima.2001.2006
David Kazhdan and Hans Wenzl, Reconstructing monoidal categories, I. M. Gel′fand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 111–136. MR 1237835
Frank Quinn, Group categories and their field theories, Proceedings of the Kirbyfest (Berkeley, CA, 1998) Geom. Topol. Monogr., vol. 2, Geom. Topol. Publ., Coventry, 1999, pp. 407–453. MR 1734419, DOI 10.2140/gtm.1999.2.407
A. N. Schellekens, Fusion rule automorphisms from integer spin simple currents, Phys. Lett. B 244 (1990), no. 2, 255–260. MR 1065268, DOI 10.1016/0370-2693(90)90065-E
Andrew Schopieray, Lie theory for fusion categories: A research primer, arXiv:1810.09055 (2018).