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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Hannah, Samuel, Laugwitz, Robert, Ros Camacho, Ana
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212009
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras. Samuel Hannah, Robert Laugwitz and Ana Ros Camacho. SIGMA 19 (2023), 075, 42 pages

We construct a separable Frobenius monoidal functor from 𝒵(Vectω|ᴴ𝐻) to 𝒵(Vectω𝐺) for any subgroup 𝐻 of 𝐺 which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in 𝒵(Vectω𝐺), recovering the classification of étale algebras in these categories by Davydo...