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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/60240
Ver los metadatos del registro completo
id |
CONICETDig_ac0ea70c655ffdb6fd01f0076915c98c |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/60240 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
network_name_str |
CONICET Digital (CONICET) |
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 |
_version_ |
1844614514882904064 |
score |
13.070432 |