Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations

Detalhes bibliográficos
Autor(a) principal: Mackaay, Marco
Data de Publicação: 2018
Outros Autores: Mazorchuk, Volodymyr, Miemietz, Vanessa, Zhang, Xiaoting
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/15114
Resumo: The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.
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spelling Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations2-categorySimple transitive 2-representationGreen relationsCoalgebra 1-morphismCotensor productThe main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.Cambridge University PressSapientiaMackaay, MarcoMazorchuk, VolodymyrMiemietz, VanessaZhang, Xiaoting2021-02-17T15:52:04Z20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/15114eng1474-748010.1017/S1474748018000555info: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:RCAAP2024-11-29T10:41:48Zoai:sapientia.ualg.pt:10400.1/15114Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-11-29T10:41:48Repositório 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 Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
title Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
spellingShingle Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
Mackaay, Marco
2-category
Simple transitive 2-representation
Green relations
Coalgebra 1-morphism
Cotensor product
title_short Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
title_full Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
title_fullStr Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
title_full_unstemmed Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
title_sort Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
author Mackaay, Marco
author_facet Mackaay, Marco
Mazorchuk, Volodymyr
Miemietz, Vanessa
Zhang, Xiaoting
author_role author
author2 Mazorchuk, Volodymyr
Miemietz, Vanessa
Zhang, Xiaoting
author2_role author
author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Mackaay, Marco
Mazorchuk, Volodymyr
Miemietz, Vanessa
Zhang, Xiaoting
dc.subject.por.fl_str_mv 2-category
Simple transitive 2-representation
Green relations
Coalgebra 1-morphism
Cotensor product
topic 2-category
Simple transitive 2-representation
Green relations
Coalgebra 1-morphism
Cotensor product
description The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
2021-02-17T15:52:04Z
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/10400.1/15114
url http://hdl.handle.net/10400.1/15114
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1474-7480
10.1017/S1474748018000555
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv mluisa.alvim@gmail.com
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