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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/58370
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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 Técnicas2025-09-29T09:36:16Zoai: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:34982025-09-29 09:36:16.784CONICET 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 |
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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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13.070432 |