Cohomology and extensions of braces

Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group st...

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Detalhes bibliográficos
Autores: Lebed, Victoria, Vendramin, Claudio Leandro
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2016
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/89065
Acesso em linha:http://hdl.handle.net/11336/89065
Access Level:Acceso aberto
Palavra-chave:BRACE
COHOMOLOGY
CYCLE SET
EXTENSION
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Cohomology and extensions of bracesLebed, VictoriaVendramin, Claudio LeandroBRACECOHOMOLOGYCYCLE SETEXTENSIONYANG-BAXTER EQUATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group structure and the (co)homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups.Fil: Lebed, Victoria. Universite de Nantes; FranciaFil: Vendramin, Claudio Leandro. 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"; ArgentinaPacific Journal Mathematics2016-09info: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/11336/89065Lebed, Victoria; Vendramin, Claudio Leandro; Cohomology and extensions of braces; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 284; 1; 9-2016; 191-2120030-8730CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://msp.org/pjm/2016/284-1/pjm-v284-n1-p07-p.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.2140/pjm.2016.284.191info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1601.01633info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:43:07Zoai:ri.conicet.gov.ar:11336/89065instacron: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:34982024-05-08 13:43:08.277CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Cohomology and extensions of braces
title Cohomology and extensions of braces
spellingShingle Cohomology and extensions of braces
Lebed, Victoria
BRACE
COHOMOLOGY
CYCLE SET
EXTENSION
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Cohomology and extensions of braces
title_full Cohomology and extensions of braces
title_fullStr Cohomology and extensions of braces
title_full_unstemmed Cohomology and extensions of braces
title_sort Cohomology and extensions of braces
dc.creator.none.fl_str_mv Lebed, Victoria
Vendramin, Claudio Leandro
author Lebed, Victoria
author_facet Lebed, Victoria
Vendramin, Claudio Leandro
author_role author
author2 Vendramin, Claudio Leandro
author2_role author
dc.subject.none.fl_str_mv BRACE
COHOMOLOGY
CYCLE SET
EXTENSION
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic BRACE
COHOMOLOGY
CYCLE SET
EXTENSION
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group structure and the (co)homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups.
publishDate 2016
dc.date.none.fl_str_mv 2016-09
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/11336/89065
Lebed, Victoria; Vendramin, Claudio Leandro; Cohomology and extensions of braces; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 284; 1; 9-2016; 191-212
0030-8730
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89065
identifier_str_mv Lebed, Victoria; Vendramin, Claudio Leandro; Cohomology and extensions of braces; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 284; 1; 9-2016; 191-212
0030-8730
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://msp.org/pjm/2016/284-1/pjm-v284-n1-p07-p.pdf
info:eu-repo/semantics/altIdentifier/doi/10.2140/pjm.2016.284.191
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1601.01633
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 Pacific Journal Mathematics
publisher.none.fl_str_mv Pacific Journal Mathematics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15.811543

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