Verma and simple modules for quantum groups at non-abelian groups

Autores
Pogorelsky, Barbara; Vay, Cristian Damian
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that a Verma module has simple head and simple socle. This provides two bijective correspondences between the set of simple modules over D and the set of simple modules over the Drinfeld double D(G). As an example, we describe the lattice of submodules of the Verma modules over the quantum group at the symmetric group S3 attached to the 12-dimensional Fomin–Kirillov algebra, computing all the simple modules and calculating their dimensions.
Fil: Pogorelsky, Barbara. Universidade Federal do Rio Grande do Sul; Brasil
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
HOPF ALGEBRAS
NICHOLS ALGEBRAS
QUANTUM GROUPS
REPRESENTATION THEORY
VERMA MODULES
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:11336/58449
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/58449
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Verma and simple modules for quantum groups at non-abelian groupsPogorelsky, BarbaraVay, Cristian DamianFOMIN-KIRILLOV ALGEBRASHOPF ALGEBRASNICHOLS ALGEBRASQUANTUM GROUPSREPRESENTATION THEORYVERMA MODULEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that a Verma module has simple head and simple socle. This provides two bijective correspondences between the set of simple modules over D and the set of simple modules over the Drinfeld double D(G). As an example, we describe the lattice of submodules of the Verma modules over the quantum group at the symmetric group S3 attached to the 12-dimensional Fomin–Kirillov algebra, computing all the simple modules and calculating their dimensions.Fil: Pogorelsky, Barbara. Universidade Federal do Rio Grande do Sul; BrasilFil: 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 Science2016-10info: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/11336/58449Pogorelsky, Barbara; Vay, Cristian Damian; Verma and simple modules for quantum groups at non-abelian groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 301; 10-2016; 423-4570001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870816308039info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2016.06.019info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:43:10Zoai:ri.conicet.gov.ar:11336/58449instacron: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:34982025-10-15 14:43:10.345CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Verma and simple modules for quantum groups at non-abelian groups
title Verma and simple modules for quantum groups at non-abelian groups
spellingShingle Verma and simple modules for quantum groups at non-abelian groups
Pogorelsky, Barbara
FOMIN-KIRILLOV ALGEBRAS
HOPF ALGEBRAS
NICHOLS ALGEBRAS
QUANTUM GROUPS
REPRESENTATION THEORY
VERMA MODULES
title_short Verma and simple modules for quantum groups at non-abelian groups
title_full Verma and simple modules for quantum groups at non-abelian groups
title_fullStr Verma and simple modules for quantum groups at non-abelian groups
title_full_unstemmed Verma and simple modules for quantum groups at non-abelian groups
title_sort Verma and simple modules for quantum groups at non-abelian groups
dc.creator.none.fl_str_mv Pogorelsky, Barbara
Vay, Cristian Damian
author Pogorelsky, Barbara
author_facet Pogorelsky, Barbara
Vay, Cristian Damian
author_role author
author2 Vay, Cristian Damian
author2_role author
dc.subject.none.fl_str_mv FOMIN-KIRILLOV ALGEBRAS
HOPF ALGEBRAS
NICHOLS ALGEBRAS
QUANTUM GROUPS
REPRESENTATION THEORY
VERMA MODULES
topic FOMIN-KIRILLOV ALGEBRAS
HOPF ALGEBRAS
NICHOLS ALGEBRAS
QUANTUM GROUPS
REPRESENTATION THEORY
VERMA MODULES
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 Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that a Verma module has simple head and simple socle. This provides two bijective correspondences between the set of simple modules over D and the set of simple modules over the Drinfeld double D(G). As an example, we describe the lattice of submodules of the Verma modules over the quantum group at the symmetric group S3 attached to the 12-dimensional Fomin–Kirillov algebra, computing all the simple modules and calculating their dimensions.
Fil: Pogorelsky, Barbara. Universidade Federal do Rio Grande do Sul; Brasil
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 Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that a Verma module has simple head and simple socle. This provides two bijective correspondences between the set of simple modules over D and the set of simple modules over the Drinfeld double D(G). As an example, we describe the lattice of submodules of the Verma modules over the quantum group at the symmetric group S3 attached to the 12-dimensional Fomin–Kirillov algebra, computing all the simple modules and calculating their dimensions.
publishDate 2016
dc.date.none.fl_str_mv 2016-10
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/11336/58449
Pogorelsky, Barbara; Vay, Cristian Damian; Verma and simple modules for quantum groups at non-abelian groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 301; 10-2016; 423-457
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58449
identifier_str_mv Pogorelsky, Barbara; Vay, Cristian Damian; Verma and simple modules for quantum groups at non-abelian groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 301; 10-2016; 423-457
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/S0001870816308039
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2016.06.019
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 13.22299

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