Classifying Grothendieck rings of pivotal fusion categories of rank four

Abstract

We classify the Classifying Grothendieck rings of pivotal fusion categories of rank four over the complex field. There are exactly fifteen, each admitting a unitary categorification. Central induction and Frobenius-Schur indicators give a uniform Frobenius-Perron dimension bound of 3600. The finite classification combines new arithmetic and twist obstructions with an exhaustive census and exact exclusion certificates.

arXiv comment22 pages; generalized indicator and associativity lemmas; clarified sphericality and Galois reductions; revised title, exposition, tables and references; classification unchanged; code, data and exact certificates in ancillary files. Comments are welcome!