On projective modules over finite quantum groups

Autores
Vay, Cristian Damian
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let (Formula presented.) be the Drinfeld double of the bosonization (Formula presented.)(V)(Formula presented.)G of a finite-dimensional Nichols algebra (Formula presented.)(V ) over a finite group G. It is known that the simple (Formula presented.)-modules are parametrized by the simple modules over (Formula presented.)(G), the Drinfeld double of G. This parametrization can be obtained by considering the head L(λ) of the Verma module M(λ) for every simple (Formula presented.)(G)-module λ. In the present work, we show that the projective (Formula presented.)-modules are filtered by Verma modules and the BGG Reciprocity [P(μ): M(λ)] = [M(λ): L(μ)] holds for the projective cover P(μ) of L(μ). We use graded characters to prove the BGG Reciprocity and obtain a graded version of it. As a by-product we show that a Verma module is simple if and only if it is projective. We also describe the tensor product between projective modules.
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
HOPF ALGEBRAS
NICHOLS ALGEBRAS
REPRESENTATION THEORY
HIGHEST WEIGHT CATEGORY
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:11336/60240

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spelling On projective modules over finite quantum groupsVay, Cristian DamianHOPF ALGEBRASNICHOLS ALGEBRASREPRESENTATION THEORYHIGHEST WEIGHT CATEGORYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let (Formula presented.) be the Drinfeld double of the bosonization (Formula presented.)(V)(Formula presented.)G of a finite-dimensional Nichols algebra (Formula presented.)(V ) over a finite group G. It is known that the simple (Formula presented.)-modules are parametrized by the simple modules over (Formula presented.)(G), the Drinfeld double of G. This parametrization can be obtained by considering the head L(λ) of the Verma module M(λ) for every simple (Formula presented.)(G)-module λ. In the present work, we show that the projective (Formula presented.)-modules are filtered by Verma modules and the BGG Reciprocity [P(μ): M(λ)] = [M(λ): L(μ)] holds for the projective cover P(μ) of L(μ). We use graded characters to prove the BGG Reciprocity and obtain a graded version of it. As a by-product we show that a Verma module is simple if and only if it is projective. We also describe the tensor product between projective modules.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; ArgentinaBirkhauser Boston Inc2017-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60240Vay, Cristian Damian; On projective modules over finite quantum groups; Birkhauser Boston Inc; Transformation Groups; 11-2017; 1-211083-43621531-586XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-017-9469-yinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-017-9469-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:47:09Zoai:ri.conicet.gov.ar:11336/60240instacron: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 10:47:09.799CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On projective modules over finite quantum groups
title On projective modules over finite quantum groups
spellingShingle On projective modules over finite quantum groups
Vay, Cristian Damian
HOPF ALGEBRAS
NICHOLS ALGEBRAS
REPRESENTATION THEORY
HIGHEST WEIGHT CATEGORY
title_short On projective modules over finite quantum groups
title_full On projective modules over finite quantum groups
title_fullStr On projective modules over finite quantum groups
title_full_unstemmed On projective modules over finite quantum groups
title_sort On projective modules over finite quantum groups
dc.creator.none.fl_str_mv Vay, Cristian Damian
author Vay, Cristian Damian
author_facet Vay, Cristian Damian
author_role author
dc.subject.none.fl_str_mv HOPF ALGEBRAS
NICHOLS ALGEBRAS
REPRESENTATION THEORY
HIGHEST WEIGHT CATEGORY
topic HOPF ALGEBRAS
NICHOLS ALGEBRAS
REPRESENTATION THEORY
HIGHEST WEIGHT CATEGORY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let (Formula presented.) be the Drinfeld double of the bosonization (Formula presented.)(V)(Formula presented.)G of a finite-dimensional Nichols algebra (Formula presented.)(V ) over a finite group G. It is known that the simple (Formula presented.)-modules are parametrized by the simple modules over (Formula presented.)(G), the Drinfeld double of G. This parametrization can be obtained by considering the head L(λ) of the Verma module M(λ) for every simple (Formula presented.)(G)-module λ. In the present work, we show that the projective (Formula presented.)-modules are filtered by Verma modules and the BGG Reciprocity [P(μ): M(λ)] = [M(λ): L(μ)] holds for the projective cover P(μ) of L(μ). We use graded characters to prove the BGG Reciprocity and obtain a graded version of it. As a by-product we show that a Verma module is simple if and only if it is projective. We also describe the tensor product between projective modules.
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 Let (Formula presented.) be the Drinfeld double of the bosonization (Formula presented.)(V)(Formula presented.)G of a finite-dimensional Nichols algebra (Formula presented.)(V ) over a finite group G. It is known that the simple (Formula presented.)-modules are parametrized by the simple modules over (Formula presented.)(G), the Drinfeld double of G. This parametrization can be obtained by considering the head L(λ) of the Verma module M(λ) for every simple (Formula presented.)(G)-module λ. In the present work, we show that the projective (Formula presented.)-modules are filtered by Verma modules and the BGG Reciprocity [P(μ): M(λ)] = [M(λ): L(μ)] holds for the projective cover P(μ) of L(μ). We use graded characters to prove the BGG Reciprocity and obtain a graded version of it. As a by-product we show that a Verma module is simple if and only if it is projective. We also describe the tensor product between projective modules.
publishDate 2017
dc.date.none.fl_str_mv 2017-11
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/11336/60240
Vay, Cristian Damian; On projective modules over finite quantum groups; Birkhauser Boston Inc; Transformation Groups; 11-2017; 1-21
1083-4362
1531-586X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60240
identifier_str_mv Vay, Cristian Damian; On projective modules over finite quantum groups; Birkhauser Boston Inc; Transformation Groups; 11-2017; 1-21
1083-4362
1531-586X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-017-9469-y
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-017-9469-y
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 Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston Inc
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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