Work

On modular categories with Frobenius–Perron dimension congruent to 2 modulo 4

Year: 2025

Type: article

Abstract: We contribute to the classification of modular categories C \mathcal {C} with F P d i m ( C ) ≡ 2 ( mod 4 ) FPdim(\mathcal {C})\equiv 2 \pmod 4 . We prove that such categories have group of invertibles of even order and that they factorize as C ≅ C ~ ⊠ P \mathcal C\cong \widetilde {\mathcal C} \boxtimes \mathcal P , where C ~ \widetilde {\mathcal C} is an odd-dimensional modular category and P \mathcal P is a pointed modular category of dimension 2. This reduces the classification of these categories to the classification of odd-dimensional modular categories. It follows that modular categories C \mathcal {C} with F P d i m ( C ) ≡ 2 ( mod 4 ) FPdim(\mathcal {C})\equiv 2 \pmod 4 of rank up to 46 (except for 34) are pointed. More generally, we prove that if C \mathcal {C} is a weakly integral modular category and p p is an odd prime dividing the order of the group of invertibles that has

Source: Proceedings of the American Mathematical Society Series B

DOI: 10.1090/bproc/231

Authors: Akshaya Chakravarthy, Agustina Czenky, Julia Plavnik

Institutions: Massachusetts Institute of Technology, University of Oregon, Vrije Universiteit Brussel, Indiana University Bloomington, Indiana University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $750

Funders: National Science Foundation, Simons Foundation, Alexander von Humboldt-Stiftung, Universität Hamburg