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Session S16 - Quantum symmetries

Monday, July 19, 17:10 ~ 17:35 UTC-3

Modular categories with transitive Galois actions

Qing Zhang

Purdue University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The absolute Galois group acts on the set of isomorphism classes of simple objects of any modular category via the characters of the fusion ring. In this talk, we consider transitive modular categories, which are modular categories with transitive Galois actions. We prove every transitive modular category admits a unique prime factorization up to the permutation of factors. The prime transitive modular categories are completely classified, which are given by certain quantum group modular categories with prime Frobenius-Schur exponents. This talk is based on joint work with S.-H. Ng and Y. Wang.

Joint work with Siu-Hung Ng (Louisiana State University) and Yilong Wang (Louisiana State University).

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