Cohomology and extensions of braces
- Autores
- Lebed, Victoria; Vendramin, Claudio Leandro
- Año de publicación
- 2016
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: Lebed, Victoria. Universite de Nantes; Francia
Fil: 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"; Argentina - Materia
-
BRACE
COHOMOLOGY
CYCLE SET
EXTENSION
YANG-BAXTER EQUATION - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/89065
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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 Técnicas2025-09-29T09:46:00Zoai: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:34982025-09-29 09:46:00.501CONICET 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 |
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 |
topic |
BRACE COHOMOLOGY CYCLE SET EXTENSION YANG-BAXTER EQUATION |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
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. Fil: Lebed, Victoria. Universite de Nantes; Francia Fil: 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"; Argentina |
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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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1844613437576970240 |
score |
13.070432 |