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

We construct a separable Frobenius monoidal functor from \(\mathcal{Z}\big(\mathsf{Vect}_H^{\omega|_H}\big)\) to \(\mathcal{Z}\big(\mathsf{Vect}_G^\omega\big)\) for any subgroup \(H\) of \(G\) which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in \...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Hannah, Samuel, Laugwitz, Robert, Ana Ros Camacho
Format: Article
Language:English
Subjects:
Algebra
Braiding
Categories
Classification
Subgroups
Tensors
Online Access:Get full text
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Summary:We construct a separable Frobenius monoidal functor from \(\mathcal{Z}\big(\mathsf{Vect}_H^{\omega|_H}\big)\) to \(\mathcal{Z}\big(\mathsf{Vect}_G^\omega\big)\) for any subgroup \(H\) of \(G\) which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in \(\mathcal{Z}\big(\mathsf{Vect}_G^\omega\big)\), recovering the classification of étale 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.
ISSN:2331-8422
DOI:10.48550/arxiv.2303.04493