Constructing Non-semisimple Modular Categories with Local Modules

Laugwitz, Robert; Walton, Chelsea

Abstract

We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previous work of Kirillov and Ostrik (Adv Math 171(2):183–227, 2002) in the semisimple setup. Examples of non-semisimple modular categories via local modules, as well as connections to the authors’ prior work on relative monoidal centers, are provided. In particular, we classify rigid Frobenius algebras in Drinfeld centers of module categories over group algebras, thus generalizing the classification by Davydov (J Algebra 323(5):1321–1348, 2010) to arbitrary characteristic.

Citation

Laugwitz, R., & Walton, C. (2023). Constructing Non-semisimple Modular Categories with Local Modules. Communications in Mathematical Physics, 403, 1363-1409. https://doi.org/10.1007/s00220-023-04824-4

• Journal Article Type: Article
• Acceptance Date: Jul 27, 2023
• Online Publication Date: Aug 19, 2023
• Publication Date: 2023-11
• Deposit Date: Jul 28, 2023
• Publicly Available Date: Aug 20, 2024
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 403
• Pages: 1363-1409
• DOI: https://doi.org/10.1007/s00220-023-04824-4
• Keywords: Mathematical Physics; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/23486370
• Publisher URL: https://link.springer.com/article/10.1007/s00220-023-04824-4
• Additional Information: This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://link.springer.com/article/10.1007/s00220-023-04824-4