Constructing Non-Semisimple Modular Categories with Relative Monoidal Centers

Laugwitz, Robert; Walton, Chelsea

Abstract

This paper is a contribution to the construction of non-semisimple modular categories. We establish when Müger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which relative monoidal centers give (non-semisimple) modular categories, and we also show that examples include representation categories of small quantum groups. We further derive conditions under which representations of more general quantum groups, braided Drinfeld doubles of Nichols algebras of diagonal type, give (non-semisimple) modular categories.

Citation

Laugwitz, R., & Walton, C. (2022). Constructing Non-Semisimple Modular Categories with Relative Monoidal Centers. International Mathematics Research Notices, 2022(20), 15826-15868. https://doi.org/10.1093/imrn/rnab097

• Journal Article Type: Article
• Acceptance Date: Mar 30, 2021
• Online Publication Date: Jul 6, 2021
• Publication Date: 2022-10
• Deposit Date: Apr 13, 2021
• Publicly Available Date: Jul 7, 2022
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Issue: 20
• Pages: 15826-15868
• DOI: https://doi.org/10.1093/imrn/rnab097
• Public URL: https://nottingham-repository.worktribe.com/output/5462977
• Publisher URL: https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnab097/6316085