A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation

Autores
Farinati, Marco Andrés; Garcia Galofre, Juliana
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(X, σ), containing the semigroup algebra A = k{X}/xy = zt : σ(x, y) = (z,t) , such that k ⊗A B ⊗A k and HomA−A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in [2,5] and other generalizations of cohomology of rack-quandle case (for example defined in [4]). This algebraic structure allows us to show the existence of an associative product in the cohomology of biquandles, and a comparison map with Hochschild (co)homology of the algebra A.
Fil: Farinati, Marco Andrés. 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
Fil: Garcia Galofre, Juliana. 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
Yang Baxter Equation
Rack
Biquandles Biracks
Cohomology
Quandles
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:11336/18914
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equationFarinati, Marco AndrésGarcia Galofre, JulianaYang Baxter EquationRackBiquandles BiracksCohomologyQuandleshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(X, σ), containing the semigroup algebra A = k{X}/xy = zt : σ(x, y) = (z,t) , such that k ⊗A B ⊗A k and HomA−A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in [2,5] and other generalizations of cohomology of rack-quandle case (for example defined in [4]). This algebraic structure allows us to show the existence of an associative product in the cohomology of biquandles, and a comparison map with Hochschild (co)homology of the algebra A.Fil: Farinati, Marco Andrés. 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"; ArgentinaFil: Garcia Galofre, Juliana. 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"; ArgentinaElsevier Science2016-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18914Farinati, Marco Andrés; Garcia Galofre, Juliana; A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation; Elsevier Science; Journal Of Pure And Applied Algebra; 220; 10; 10-2016; 3454-34750022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2016.04.010info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022404916300184info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1508.07970info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:09:45Zoai:ri.conicet.gov.ar:11336/18914instacron: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:34982025-11-05 10:09:45.366CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
title A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
spellingShingle A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
Farinati, Marco Andrés
Yang Baxter Equation
Rack
Biquandles Biracks
Cohomology
Quandles
title_short A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
title_full A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
title_fullStr A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
title_full_unstemmed A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
title_sort A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation
dc.creator.none.fl_str_mv Farinati, Marco Andrés
Garcia Galofre, Juliana
author Farinati, Marco Andrés
author_facet Farinati, Marco Andrés
Garcia Galofre, Juliana
author_role author
author2 Garcia Galofre, Juliana
author2_role author
dc.subject.none.fl_str_mv Yang Baxter Equation
Rack
Biquandles Biracks
Cohomology
Quandles
topic Yang Baxter Equation
Rack
Biquandles Biracks
Cohomology
Quandles
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(X, σ), containing the semigroup algebra A = k{X}/xy = zt : σ(x, y) = (z,t) , such that k ⊗A B ⊗A k and HomA−A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in [2,5] and other generalizations of cohomology of rack-quandle case (for example defined in [4]). This algebraic structure allows us to show the existence of an associative product in the cohomology of biquandles, and a comparison map with Hochschild (co)homology of the algebra A.
Fil: Farinati, Marco Andrés. 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
Fil: Garcia Galofre, Juliana. 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 For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(X, σ), containing the semigroup algebra A = k{X}/xy = zt : σ(x, y) = (z,t) , such that k ⊗A B ⊗A k and HomA−A(B, k) are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in [2,5] and other generalizations of cohomology of rack-quandle case (for example defined in [4]). This algebraic structure allows us to show the existence of an associative product in the cohomology of biquandles, and a comparison map with Hochschild (co)homology of the algebra A.
publishDate 2016
dc.date.none.fl_str_mv 2016-10
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/11336/18914
Farinati, Marco Andrés; Garcia Galofre, Juliana; A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation; Elsevier Science; Journal Of Pure And Applied Algebra; 220; 10; 10-2016; 3454-3475
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18914
identifier_str_mv Farinati, Marco Andrés; Garcia Galofre, Juliana; A differential bialgebra associated to a set theoretical solution of the Yang–Baxter equation; Elsevier Science; Journal Of Pure And Applied Algebra; 220; 10; 10-2016; 3454-3475
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2016.04.010
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022404916300184
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1508.07970
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
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 13.087074

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