Simple transitive 2-representations via (Co-)Algebra 1-Morphisms

Detalhes bibliográficos
Autor(a) principal: Mackaay, Marco
Data de Publicação: 2019
Outros Autores: Mazorchuk, Volodymyr, Miemietz, Vanessa, Tubbenhauer, Daniel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/14484
Resumo: For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.
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spelling Simple transitive 2-representations via (Co-)Algebra 1-MorphismsHopf-AlgebrasCategoriesBimodulesFor any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.Swedish Research CouncilSwedish Research CouncilKnut and Alice Wallenberg StiftelseKnut & Alice Wallenberg FoundationGoran Gustafsson StiftelseUppsala UniversityHausdorff Center for Mathematics (HCM) in BonnIndiana Univ Math JournalSapientiaMackaay, MarcoMazorchuk, VolodymyrMiemietz, VanessaTubbenhauer, Daniel2020-07-24T10:53:22Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/14484eng0022-251810.1512/iumj.2019.68.7554info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:26:47Zoai:sapientia.ualg.pt:10400.1/14484Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:05:31.067280Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
title Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
spellingShingle Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
Mackaay, Marco
Hopf-Algebras
Categories
Bimodules
title_short Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
title_full Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
title_fullStr Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
title_full_unstemmed Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
title_sort Simple transitive 2-representations via (Co-)Algebra 1-Morphisms
author Mackaay, Marco
author_facet Mackaay, Marco
Mazorchuk, Volodymyr
Miemietz, Vanessa
Tubbenhauer, Daniel
author_role author
author2 Mazorchuk, Volodymyr
Miemietz, Vanessa
Tubbenhauer, Daniel
author2_role author
author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Mackaay, Marco
Mazorchuk, Volodymyr
Miemietz, Vanessa
Tubbenhauer, Daniel
dc.subject.por.fl_str_mv Hopf-Algebras
Categories
Bimodules
topic Hopf-Algebras
Categories
Bimodules
description For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
2020-07-24T10:53:22Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.1/14484
url http://hdl.handle.net/10400.1/14484
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-2518
10.1512/iumj.2019.68.7554
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Indiana Univ Math Journal
publisher.none.fl_str_mv Indiana Univ Math Journal
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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instacron_str RCAAP
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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