Invertible bimodule categories over the representation category of a Hopf algebra

For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal (H) → BrPic(Rep(H)), from the group of equivalence classes of H-biGalois objects to the group of equivalence classes of invertible exact Rep(H)-bimodule categories. We discuss the injectivity of this map. We exempli...

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Autores principales:	Femić, Bojana, Mejía Castaño, Adriana, Mombelli, Juan Martín
Formato:	article
Lenguaje:	Inglés
Publicado:	2022
Materias:	Categorías tensoriales Álgebras de Hopf Representaciones de categorías tensoriales Grupo de Brauer-Picard Monoidal categories Symmetric monoidal categories Brauer-Picard group Tensor category biGalois object
Acceso en línea:	http://hdl.handle.net/11086/28253 https://doi.org/10.48550/arXiv.1402.2955
Aporte de:	Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba

id	I10-R141-11086-28253
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institution	Universidad Nacional de Córdoba
institution_str	I-10
repository_str	R-141
collection	Repositorio Digital Universitario (UNC)
language	Inglés
topic	Categorías tensoriales Álgebras de Hopf Representaciones de categorías tensoriales Grupo de Brauer-Picard Monoidal categories Symmetric monoidal categories Brauer-Picard group Tensor category biGalois object
spellingShingle	Categorías tensoriales Álgebras de Hopf Representaciones de categorías tensoriales Grupo de Brauer-Picard Monoidal categories Symmetric monoidal categories Brauer-Picard group Tensor category biGalois object Femić, Bojana Mejía Castaño, Adriana Mombelli, Juan Martín Invertible bimodule categories over the representation category of a Hopf algebra
topic_facet	Categorías tensoriales Álgebras de Hopf Representaciones de categorías tensoriales Grupo de Brauer-Picard Monoidal categories Symmetric monoidal categories Brauer-Picard group Tensor category biGalois object
description	For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal (H) → BrPic(Rep(H)), from the group of equivalence classes of H-biGalois objects to the group of equivalence classes of invertible exact Rep(H)-bimodule categories. We discuss the injectivity of this map. We exemplify in the case H = Tq is a Taft Hopf algebra and for this we classify all exact indecomposable Rep(Tq)- bimodule categories.
format	article
author	Femić, Bojana Mejía Castaño, Adriana Mombelli, Juan Martín
author_facet	Femić, Bojana Mejía Castaño, Adriana Mombelli, Juan Martín
author_sort	Femić, Bojana
title	Invertible bimodule categories over the representation category of a Hopf algebra
title_short	Invertible bimodule categories over the representation category of a Hopf algebra
title_full	Invertible bimodule categories over the representation category of a Hopf algebra
title_fullStr	Invertible bimodule categories over the representation category of a Hopf algebra
title_full_unstemmed	Invertible bimodule categories over the representation category of a Hopf algebra
title_sort	invertible bimodule categories over the representation category of a hopf algebra
publishDate	2022
url	http://hdl.handle.net/11086/28253 https://doi.org/10.48550/arXiv.1402.2955
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bdutipo_str	Repositorios
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Invertible bimodule categories over the representation category of a Hopf algebra

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