Constructing non-semisimple modular categories with local modules
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 A. Kirillov, Jr. and V. Ostrik [Adv. Math. 171 (2002), no. 2] 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 A. Davydov [J. Algebra 323 (2010), no. 5] to arbitrary characteristic.
Cite
@article{arxiv.2202.08644,
title = {Constructing non-semisimple modular categories with local modules},
author = {Robert Laugwitz and Chelsea Walton},
journal= {arXiv preprint arXiv:2202.08644},
year = {2025}
}
Comments
v2: 43 pages. Updated Section 6.3 and acknowledgements. Submitted. v3: 45 pages. Final version to appear in Comm. Math. Phys