The character algebra for module categories over hopf algebras

Given a finite-dimensional Hopf algebra H and an exact indecomposable module category M over Rep(H), we explicitly compute the adjoint algebra A_M as an object in the category of Yetter-Drinfeld modules over H, and the space of class functions CF(M) associated to M, as introduced by K. Shimizu (2020...

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Detalhes bibliográficos
Autores: Bortolussi, Noelia Belén, Mombelli, Juan Martín
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/175897
Acesso em linha:http://hdl.handle.net/11336/175897
Access Level:acceso abierto
Palavra-chave:HOPF ALGEBRA
MODULE CATEGORY
TENSOR CATEGORY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:Given a finite-dimensional Hopf algebra H and an exact indecomposable module category M over Rep(H), we explicitly compute the adjoint algebra A_M as an object in the category of Yetter-Drinfeld modules over H, and the space of class functions CF(M) associated to M, as introduced by K. Shimizu (2020). We use our construction to describe these algebras when H is a group algebra and a dual group algebra. This result allows us to compute the adjoint algebra for certain group-theoretical fusion categories.