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Constructing Non-semisimple Modular Categories with Local Modules.
- Source :
-
Communications in Mathematical Physics . Nov2023, Vol. 403 Issue 3, p1363-1409. 47p. - Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FROBENIUS algebras
*DRINFELD modules
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 403
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 172893449
- Full Text :
- https://doi.org/10.1007/s00220-023-04824-4