Simple modules of small quantum groups at dihedral groups

Autores
García, Gastón Andrés; Vay, Cristian Damian
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of bosonizations of finite-dimensional Nichols algebras over the dihedral groups D4t with t 3. To this end, we develop new techniques that can be applied to Nichols algebras over any Hopf algebra. Namely, we explain how to construct recursively irreducible representations when the Nichols algebra is generated by a decomposable module, and show that the highest-weight of minimum degree in a Verma module determines its socle. We also prove that tensoring a simple module by a rigid simple module gives a semisimple module.
Fil: García, Gastón Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina
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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
HOPF ALGEBRAS
REPRESENTATION THEORY
NICHOLS ALGEBRAS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/257150
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Simple modules of small quantum groups at dihedral groupsGarcía, Gastón AndrésVay, Cristian DamianHOPF ALGEBRASREPRESENTATION THEORYNICHOLS ALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of bosonizations of finite-dimensional Nichols algebras over the dihedral groups D4t with t 3. To this end, we develop new techniques that can be applied to Nichols algebras over any Hopf algebra. Namely, we explain how to construct recursively irreducible representations when the Nichols algebra is generated by a decomposable module, and show that the highest-weight of minimum degree in a Verma module determines its socle. We also prove that tensoring a simple module by a rigid simple module gives a semisimple module.Fil: García, Gastón Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; ArgentinaFil: 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaUniversität Bielefeld2024-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/257150García, Gastón Andrés; Vay, Cristian Damian; Simple modules of small quantum groups at dihedral groups; Universität Bielefeld; Documenta Mathematica; 29; 1; 2-2024; 1-381431-0643CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ems.press/journals/dm/articles/14275127info:eu-repo/semantics/altIdentifier/doi/10.4171/DM/942info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:52Zoai:ri.conicet.gov.ar:11336/257150instacron: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 09:33:53.081CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Simple modules of small quantum groups at dihedral groups
title Simple modules of small quantum groups at dihedral groups
spellingShingle Simple modules of small quantum groups at dihedral groups
García, Gastón Andrés
HOPF ALGEBRAS
REPRESENTATION THEORY
NICHOLS ALGEBRAS
title_short Simple modules of small quantum groups at dihedral groups
title_full Simple modules of small quantum groups at dihedral groups
title_fullStr Simple modules of small quantum groups at dihedral groups
title_full_unstemmed Simple modules of small quantum groups at dihedral groups
title_sort Simple modules of small quantum groups at dihedral groups
dc.creator.none.fl_str_mv García, Gastón Andrés
Vay, Cristian Damian
author García, Gastón Andrés
author_facet García, Gastón Andrés
Vay, Cristian Damian
author_role author
author2 Vay, Cristian Damian
author2_role author
dc.subject.none.fl_str_mv HOPF ALGEBRAS
REPRESENTATION THEORY
NICHOLS ALGEBRAS
topic HOPF ALGEBRAS
REPRESENTATION THEORY
NICHOLS ALGEBRAS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of bosonizations of finite-dimensional Nichols algebras over the dihedral groups D4t with t 3. To this end, we develop new techniques that can be applied to Nichols algebras over any Hopf algebra. Namely, we explain how to construct recursively irreducible representations when the Nichols algebra is generated by a decomposable module, and show that the highest-weight of minimum degree in a Verma module determines its socle. We also prove that tensoring a simple module by a rigid simple module gives a semisimple module.
Fil: García, Gastón Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina
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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of bosonizations of finite-dimensional Nichols algebras over the dihedral groups D4t with t 3. To this end, we develop new techniques that can be applied to Nichols algebras over any Hopf algebra. Namely, we explain how to construct recursively irreducible representations when the Nichols algebra is generated by a decomposable module, and show that the highest-weight of minimum degree in a Verma module determines its socle. We also prove that tensoring a simple module by a rigid simple module gives a semisimple module.
publishDate 2024
dc.date.none.fl_str_mv 2024-02
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/11336/257150
García, Gastón Andrés; Vay, Cristian Damian; Simple modules of small quantum groups at dihedral groups; Universität Bielefeld; Documenta Mathematica; 29; 1; 2-2024; 1-38
1431-0643
CONICET Digital
CONICET
url http://hdl.handle.net/11336/257150
identifier_str_mv García, Gastón Andrés; Vay, Cristian Damian; Simple modules of small quantum groups at dihedral groups; Universität Bielefeld; Documenta Mathematica; 29; 1; 2-2024; 1-38
1431-0643
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://ems.press/journals/dm/articles/14275127
info:eu-repo/semantics/altIdentifier/doi/10.4171/DM/942
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universität Bielefeld
publisher.none.fl_str_mv Universität Bielefeld
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 13.070432

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