Graded braided commutativity in Hochschild cohomology

Autores
Cóppola, Claudio Javier; Solotar, Andrea Leonor
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove the graded braided commutativity of the Hochschild cohomology of A with trivial coefficients, where A is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of A as A-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of A-bimodules. We also prove that the Hochschild complex of a braided bialgebra A in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology.
Fil: Cóppola, Claudio Javier. Universidad de la República; Uruguay
Fil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Braiding
Hochschild
cohomology
product
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/255043
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Graded braided commutativity in Hochschild cohomologyCóppola, Claudio JavierSolotar, Andrea LeonorBraidingHochschildcohomologyproducthttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove the graded braided commutativity of the Hochschild cohomology of A with trivial coefficients, where A is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of A as A-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of A-bimodules. We also prove that the Hochschild complex of a braided bialgebra A in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology.Fil: Cóppola, Claudio Javier. Universidad de la República; UruguayFil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaMount Allison University2024-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/255043Cóppola, Claudio Javier; Solotar, Andrea Leonor; Graded braided commutativity in Hochschild cohomology; Mount Allison University; Theory And Applications Of Categories; 41; 46; 10-2024; 1596-16431201-561XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/46/41-46abs.htmlinfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/46/41-46.pdfinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2211.11985info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:50Zoai:ri.conicet.gov.ar:11336/255043instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:35:50.909CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Graded braided commutativity in Hochschild cohomology
title Graded braided commutativity in Hochschild cohomology
spellingShingle Graded braided commutativity in Hochschild cohomology
Cóppola, Claudio Javier
Braiding
Hochschild
cohomology
product
title_short Graded braided commutativity in Hochschild cohomology
title_full Graded braided commutativity in Hochschild cohomology
title_fullStr Graded braided commutativity in Hochschild cohomology
title_full_unstemmed Graded braided commutativity in Hochschild cohomology
title_sort Graded braided commutativity in Hochschild cohomology
dc.creator.none.fl_str_mv Cóppola, Claudio Javier
Solotar, Andrea Leonor
author Cóppola, Claudio Javier
author_facet Cóppola, Claudio Javier
Solotar, Andrea Leonor
author_role author
author2 Solotar, Andrea Leonor
author2_role author
dc.subject.none.fl_str_mv Braiding
Hochschild
cohomology
product
topic Braiding
Hochschild
cohomology
product
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove the graded braided commutativity of the Hochschild cohomology of A with trivial coefficients, where A is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of A as A-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of A-bimodules. We also prove that the Hochschild complex of a braided bialgebra A in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology.
Fil: Cóppola, Claudio Javier. Universidad de la República; Uruguay
Fil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We prove the graded braided commutativity of the Hochschild cohomology of A with trivial coefficients, where A is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of A as A-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of A-bimodules. We also prove that the Hochschild complex of a braided bialgebra A in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology.
publishDate 2024
dc.date.none.fl_str_mv 2024-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/255043
Cóppola, Claudio Javier; Solotar, Andrea Leonor; Graded braided commutativity in Hochschild cohomology; Mount Allison University; Theory And Applications Of Categories; 41; 46; 10-2024; 1596-1643
1201-561X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/255043
identifier_str_mv Cóppola, Claudio Javier; Solotar, Andrea Leonor; Graded braided commutativity in Hochschild cohomology; Mount Allison University; Theory And Applications Of Categories; 41; 46; 10-2024; 1596-1643
1201-561X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/46/41-46abs.html
info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/41/46/41-46.pdf
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2211.11985
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Mount Allison University
publisher.none.fl_str_mv Mount Allison University
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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