Algebraic realization of noncommutative near-group fusion categories

Izumi, Masaki; Tucker, Henry

doi:10.2140/ant.2021.15.1077

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Algebraic realization of noncommutative near-group fusion categories

Masaki Izumi and Henry Tucker

Vol. 15 (2021), No. 5, 1077–1093

DOI: 10.2140/ant.2021.15.1077

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.

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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

Vol. 15, No. 5, 2021