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On odd-dimensional modular tensor categories

Agustina Czenky and Julia Plavnik

Vol. 16 (2022), No. 8, 1919–1939

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.

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modular tensor categories, classification, odd-dimensional, weakly group theoretical
Mathematical Subject Classification
Primary: 18M20
Received: 9 September 2020
Revised: 18 October 2021
Accepted: 13 December 2021
Published: 29 November 2022
Agustina Czenky
Department of Mathematics
University of Oregon
Eugene, OR
United States
Julia Plavnik
Department of Mathematics
Indiana University
Bloomington, IN
United States