On odd-dimensional modular tensor categories

2020/07/03 by Agustina Czenky, Czenky, Agustina, Julia Plavnik +1 · 3 citations
Mathematics · #18M20 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2007.01477

openalex publication_date 2020/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study odd-dimensional modular tensor categories and maximally non-self 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 MNSD modular tensor categories of ranks 13 and 15 are pointed. In addition, we show that MNSD tensor categories of ranks 17, 19, 21 and 23 are either pointed or perfect.

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• Generalized Witt and Morita equivalences
• A new criterion for integral modular categorification
• Classifying integral Grothendieck rings up to rank 5 and beyond

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