Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras

Hannah, Samuel; Laugwitz, Robert; Ros Camacho, Ana

Abstract

We construct a separable Frobenius monoidal functor from Z Vect ω| H H to Z Vect ω G for any subgroup H of G which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in Z Vect ω G , recovering the classification ofétale ofétale algebras in these categories by Davydov-Simmons [J. Algebra 471 (2017), 149-175, arXiv:1603.04650] and generalizing their classification to algebraically closed fields of arbitrary characteristic. Categories of local modules over such algebras are modular tensor categories by results of Kirillov-Ostrik [Adv. Math. 171 (2002), 183-227, arXiv:math.QA/0101219] in the semisimple case and Laugwitz-Walton [Comm. Math. Phys., to appear, arXiv:2202.08644] in the general case.

• Journal Article Type: Article
• Acceptance Date: Sep 26, 2023
• Online Publication Date: Oct 12, 2023
• Publication Date: 2023
• Deposit Date: Oct 13, 2023
• Publicly Available Date: Oct 13, 2023
• Journal: Symmetry, Integrability and Geometry: Methods and Applications
• Electronic ISSN: 1815-0659
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Article Number: 075
• DOI: https://doi.org/10.3842/sigma.2023.075
• Keywords: Frobenius monoidal functor; Frobenius algebra; Dijkgraaf-Witten category; local module; modular tensor category; étale algebra.
• Public URL: https://nottingham-repository.worktribe.com/output/25946128