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

Bibliographic Details
Main Author: Mackaay, Marco
Publication Date: 2018
Other Authors: Mazorchuk, Volodymyr, Miemietz, Vanessa, Zhang, Xiaoting
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.1/15114
Summary: 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.
id RCAP_037e73c9ad274a88ec84cf1716ffedfb
oai_identifier_str oai:sapientia.ualg.pt:10400.1/15114
network_acronym_str RCAP
network_name_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository_id_str https://opendoar.ac.uk/repository/7160
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-18T17:32:29Zoai:sapientia.ualg.pt:10400.1/15114Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T20:25:54.308391Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833598656197951488

Similar Items