Vol. 15, No. 5, 2021

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Algebraic realization of noncommutative near-group fusion categories

Masaki Izumi and Henry Tucker

Vol. 15 (2021), No. 5, 1077–1093
Abstract

Noncommutative near-group fusion categories were completely classified in the previous work of the first author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group theoretical though the corresponding pointed categories were not identified. In this note we give a purely algebraic construction of the noncommutative near-group fusion categories starting from pointed categories categorically Morita equivalent to them.

Keywords
tensor categories, fusion categories, Hopf algebras, quasi-Hopf algebras, Frobenius–Schur indicators, near-group categories, group cohomology
Mathematical Subject Classification
Primary: 18M20, 16T05
Milestones
Received: 13 August 2019
Revised: 14 September 2020
Accepted: 11 November 2020
Published: 30 June 2021
Authors
Masaki Izumi
Graduate School of Science
Kyoto University
Kyoto
Japan
Henry Tucker
Department of Mathematics
University of California, San Diego
La Jolla, CA
United States