Homological invariants relating the super Jordan plane to the Virasoro algebra

Nichols algebras are an important tool for the classification of Hopf algebras. Within those with finite GK dimension, we study homological invariants of the super Jordan plane, that is, the Nichols algebra A=B(V(−1,2)). These invariants are Hochschild homology, the Hochschild cohomology algebra, th...

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Detalles Bibliográficos
Autores: Solotar, Andrea Leonor, Reca, Sebastián Gustavo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/88937
Acceso en línea:http://hdl.handle.net/11336/88937
Access Level:acceso abierto
Palabra clave:GERSTENHABER BRACKET
HOCHSCHILD COHOMOLOGY
NICHOLS ALGEBRA
VIRASORO ALGEBRA
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Homological invariants relating the super Jordan plane to the Virasoro algebraSolotar, Andrea LeonorReca, Sebastián GustavoGERSTENHABER BRACKETHOCHSCHILD COHOMOLOGYNICHOLS ALGEBRAVIRASORO ALGEBRAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Nichols algebras are an important tool for the classification of Hopf algebras. Within those with finite GK dimension, we study homological invariants of the super Jordan plane, that is, the Nichols algebra A=B(V(−1,2)). These invariants are Hochschild homology, the Hochschild cohomology algebra, the Lie structure of the first cohomology space – which is a Lie subalgebra of the Virasoro algebra – and its representations Hn(A,A) and also the Yoneda algebra. We prove that the algebra A is K2. Moreover, we prove that the Yoneda algebra of the bosonization A#kZ of A is also finitely generated, but not K2.Fil: Solotar, Andrea Leonor. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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: Reca, Sebastián Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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"; ArgentinaAcademic Press Inc Elsevier Science2018-08info: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/11336/88937Solotar, Andrea Leonor; Reca, Sebastián Gustavo; Homological invariants relating the super Jordan plane to the Virasoro algebra; Academic Press Inc Elsevier Science; Journal of Algebra; 507; 8-2018; 120-1850021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2018.04.008info:eu-repo/semantics/altIdentifier/url/sciencedirect.com/science/article/pii/S0021869318302564info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:11:19Zoai:ri.conicet.gov.ar:11336/88937instacron: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 14:11:19.4CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Homological invariants relating the super Jordan plane to the Virasoro algebra
title Homological invariants relating the super Jordan plane to the Virasoro algebra
spellingShingle Homological invariants relating the super Jordan plane to the Virasoro algebra
Solotar, Andrea Leonor
GERSTENHABER BRACKET
HOCHSCHILD COHOMOLOGY
NICHOLS ALGEBRA
VIRASORO ALGEBRA
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Homological invariants relating the super Jordan plane to the Virasoro algebra
title_full Homological invariants relating the super Jordan plane to the Virasoro algebra
title_fullStr Homological invariants relating the super Jordan plane to the Virasoro algebra
title_full_unstemmed Homological invariants relating the super Jordan plane to the Virasoro algebra
title_sort Homological invariants relating the super Jordan plane to the Virasoro algebra
dc.creator.none.fl_str_mv Solotar, Andrea Leonor
Reca, Sebastián Gustavo
author Solotar, Andrea Leonor
author_facet Solotar, Andrea Leonor
Reca, Sebastián Gustavo
author_role author
author2 Reca, Sebastián Gustavo
author2_role author
dc.subject.none.fl_str_mv GERSTENHABER BRACKET
HOCHSCHILD COHOMOLOGY
NICHOLS ALGEBRA
VIRASORO ALGEBRA
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic GERSTENHABER BRACKET
HOCHSCHILD COHOMOLOGY
NICHOLS ALGEBRA
VIRASORO ALGEBRA
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Nichols algebras are an important tool for the classification of Hopf algebras. Within those with finite GK dimension, we study homological invariants of the super Jordan plane, that is, the Nichols algebra A=B(V(−1,2)). These invariants are Hochschild homology, the Hochschild cohomology algebra, the Lie structure of the first cohomology space – which is a Lie subalgebra of the Virasoro algebra – and its representations Hn(A,A) and also the Yoneda algebra. We prove that the algebra A is K2. Moreover, we prove that the Yoneda algebra of the bosonization A#kZ of A is also finitely generated, but not K2.
publishDate 2018
dc.date.none.fl_str_mv 2018-08
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/11336/88937
Solotar, Andrea Leonor; Reca, Sebastián Gustavo; Homological invariants relating the super Jordan plane to the Virasoro algebra; Academic Press Inc Elsevier Science; Journal of Algebra; 507; 8-2018; 120-185
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88937
identifier_str_mv Solotar, Andrea Leonor; Reca, Sebastián Gustavo; Homological invariants relating the super Jordan plane to the Virasoro algebra; Academic Press Inc Elsevier Science; Journal of Algebra; 507; 8-2018; 120-185
0021-8693
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.jalgebra.2018.04.008
info:eu-repo/semantics/altIdentifier/url/sciencedirect.com/science/article/pii/S0021869318302564
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
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 15.81155

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