The cohomology ring of the 12-dimensional Fomin-Kirillov algebra

Autores
Stefan, Dragos; Vay, Cristian Damian
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The 12-dimensional Fomin-Kirillov algebra FK3 is defined as the quadratic algebra with generators a, b and c which satisfy the relations a2=b2=c2=0 and ab+bc+ca=0=ba+cb+ac. By a result of A. Milinski and H.-J. Schneider, this algebra is isomorphic to the Nichols algebra associated to the Yetter-Drinfeld module V, over the symmetric group S3, corresponding to the conjugacy class of all transpositions and the sign representation. Exploiting this identification, we compute the cohomology ring ExtFK3*(k,k), showing that it is a polynomial ring S[X] with coefficients in the symmetric braided algebra of V. As an application we also compute the cohomology rings of the bosonization FK3#kS3 and of its dual, which are 72-dimensional ordinary Hopf algebras.
Fil: Stefan, Dragos. University Of Bucharest; Rumania
Fil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
FOMIN-KIRILLOV ALGEBRAS
NICHOLS BIALGEBRAS
YONEDA RING
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:11336/58370
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The cohomology ring of the 12-dimensional Fomin-Kirillov algebraStefan, DragosVay, Cristian DamianFOMIN-KIRILLOV ALGEBRASNICHOLS BIALGEBRASYONEDA RINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The 12-dimensional Fomin-Kirillov algebra FK3 is defined as the quadratic algebra with generators a, b and c which satisfy the relations a2=b2=c2=0 and ab+bc+ca=0=ba+cb+ac. By a result of A. Milinski and H.-J. Schneider, this algebra is isomorphic to the Nichols algebra associated to the Yetter-Drinfeld module V, over the symmetric group S3, corresponding to the conjugacy class of all transpositions and the sign representation. Exploiting this identification, we compute the cohomology ring ExtFK3*(k,k), showing that it is a polynomial ring S[X] with coefficients in the symmetric braided algebra of V. As an application we also compute the cohomology rings of the bosonization FK3#kS3 and of its dual, which are 72-dimensional ordinary Hopf algebras.Fil: Stefan, Dragos. University Of Bucharest; RumaniaFil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaAcademic Press Inc Elsevier Science2016-03info: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/11336/58370Stefan, Dragos; Vay, Cristian Damian; The cohomology ring of the 12-dimensional Fomin-Kirillov algebra; Academic Press Inc Elsevier Science; Advances in Mathematics; 291; 3-2016; 584-6200001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870816000190info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2016.01.001info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1404.5101info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:34:41Zoai:ri.conicet.gov.ar:11336/58370instacron: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:34982025-11-12 09:34:42.258CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
title The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
spellingShingle The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
Stefan, Dragos
FOMIN-KIRILLOV ALGEBRAS
NICHOLS BIALGEBRAS
YONEDA RING
title_short The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
title_full The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
title_fullStr The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
title_full_unstemmed The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
title_sort The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
dc.creator.none.fl_str_mv Stefan, Dragos
Vay, Cristian Damian
author Stefan, Dragos
author_facet Stefan, Dragos
Vay, Cristian Damian
author_role author
author2 Vay, Cristian Damian
author2_role author
dc.subject.none.fl_str_mv FOMIN-KIRILLOV ALGEBRAS
NICHOLS BIALGEBRAS
YONEDA RING
topic FOMIN-KIRILLOV ALGEBRAS
NICHOLS BIALGEBRAS
YONEDA RING
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The 12-dimensional Fomin-Kirillov algebra FK3 is defined as the quadratic algebra with generators a, b and c which satisfy the relations a2=b2=c2=0 and ab+bc+ca=0=ba+cb+ac. By a result of A. Milinski and H.-J. Schneider, this algebra is isomorphic to the Nichols algebra associated to the Yetter-Drinfeld module V, over the symmetric group S3, corresponding to the conjugacy class of all transpositions and the sign representation. Exploiting this identification, we compute the cohomology ring ExtFK3*(k,k), showing that it is a polynomial ring S[X] with coefficients in the symmetric braided algebra of V. As an application we also compute the cohomology rings of the bosonization FK3#kS3 and of its dual, which are 72-dimensional ordinary Hopf algebras.
Fil: Stefan, Dragos. University Of Bucharest; Rumania
Fil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description The 12-dimensional Fomin-Kirillov algebra FK3 is defined as the quadratic algebra with generators a, b and c which satisfy the relations a2=b2=c2=0 and ab+bc+ca=0=ba+cb+ac. By a result of A. Milinski and H.-J. Schneider, this algebra is isomorphic to the Nichols algebra associated to the Yetter-Drinfeld module V, over the symmetric group S3, corresponding to the conjugacy class of all transpositions and the sign representation. Exploiting this identification, we compute the cohomology ring ExtFK3*(k,k), showing that it is a polynomial ring S[X] with coefficients in the symmetric braided algebra of V. As an application we also compute the cohomology rings of the bosonization FK3#kS3 and of its dual, which are 72-dimensional ordinary Hopf algebras.
publishDate 2016
dc.date.none.fl_str_mv 2016-03
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/11336/58370
Stefan, Dragos; Vay, Cristian Damian; The cohomology ring of the 12-dimensional Fomin-Kirillov algebra; Academic Press Inc Elsevier Science; Advances in Mathematics; 291; 3-2016; 584-620
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58370
identifier_str_mv Stefan, Dragos; Vay, Cristian Damian; The cohomology ring of the 12-dimensional Fomin-Kirillov algebra; Academic Press Inc Elsevier Science; Advances in Mathematics; 291; 3-2016; 584-620
0001-8708
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://www.sciencedirect.com/science/article/pii/S0001870816000190
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2016.01.001
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1404.5101
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc 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 12.976206

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