On odd-dimensional modular tensor categories

Czenky, Agustina; Plavnik, Julia

doi:10.2140/ant.2022.16.1919

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On odd-dimensional modular tensor categories

Agustina Czenky and Julia Plavnik

Vol. 16 (2022), No. 8, 1919–1939

DOI: 10.2140/ant.2022.16.1919

Abstract

We study odd-dimensional modular tensor categories and maximally nonself dual (MNSD) modular tensor categories of low rank. We give lower bounds for the ranks of modular tensor categories in terms of the rank of the adjoint subcategory and the order of the group of invertible objects. As an application of these results, we prove that odd-dimensional modular tensor categories of ranks 13 and 15 are pointed. In addition, we show that odd-dimensional tensor categories of ranks 17, 19, 21 and 23 are either pointed or perfect.

Keywords

modular tensor categories, classification, odd-dimensional, weakly group theoretical

Mathematical Subject Classification

Primary: 18M20

Milestones

Received: 9 September 2020

Revised: 18 October 2021

Accepted: 13 December 2021

Published: 29 November 2022

Authors

Agustina Czenky
Department of Mathematics University of Oregon Eugene, OR United States

Julia Plavnik
Department of Mathematics Indiana University Bloomington, IN United States

Vol. 16, No. 8, 2022