Twisted Semigroup Algebras

Autores
Rigal, Laurent; Zadunaisky Bustillos, Pablo Mauricio
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric variety over k, and we refer to the twists of k[S] as quantum affine toric varieties. We show that every quantum affine toric variety has a “dense quantum torus”, in the sense that it has a localization isomorphic to a quantum torus. We study quantum affine toric varieties and show that many geometric regularity properties of the original toric variety survive the deformation process.
Fil: Rigal, Laurent. Université de Saint-Etienne; Argentina
Fil: Zadunaisky Bustillos, Pablo Mauricio. 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"; Argentina
Materia
Noncommutative geometry
Artin-Schelter regularity
2-cocycle twists
Zhang twists
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:11336/116933
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/116933
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Twisted Semigroup AlgebrasRigal, LaurentZadunaisky Bustillos, Pablo MauricioNoncommutative geometryArtin-Schelter regularity2-cocycle twistsZhang twistshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric variety over k, and we refer to the twists of k[S] as quantum affine toric varieties. We show that every quantum affine toric variety has a “dense quantum torus”, in the sense that it has a localization isomorphic to a quantum torus. We study quantum affine toric varieties and show that many geometric regularity properties of the original toric variety survive the deformation process.Fil: Rigal, Laurent. Université de Saint-Etienne; ArgentinaFil: Zadunaisky Bustillos, Pablo Mauricio. 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"; ArgentinaSpringer2015-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/116933Rigal, Laurent; Zadunaisky Bustillos, Pablo Mauricio; Twisted Semigroup Algebras; Springer; Algebras and Representation Theory; 18; 5; 8-2015; 1155-11861386-923XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10468-015-9525-zinfo:eu-repo/semantics/altIdentifier/doi/10.1007%2Fs10468-015-9525-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:11:52Zoai:ri.conicet.gov.ar:11336/116933instacron: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:34982025-10-22 11:11:52.728CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Twisted Semigroup Algebras
title Twisted Semigroup Algebras
spellingShingle Twisted Semigroup Algebras
Rigal, Laurent
Noncommutative geometry
Artin-Schelter regularity
2-cocycle twists
Zhang twists
title_short Twisted Semigroup Algebras
title_full Twisted Semigroup Algebras
title_fullStr Twisted Semigroup Algebras
title_full_unstemmed Twisted Semigroup Algebras
title_sort Twisted Semigroup Algebras
dc.creator.none.fl_str_mv Rigal, Laurent
Zadunaisky Bustillos, Pablo Mauricio
author Rigal, Laurent
author_facet Rigal, Laurent
Zadunaisky Bustillos, Pablo Mauricio
author_role author
author2 Zadunaisky Bustillos, Pablo Mauricio
author2_role author
dc.subject.none.fl_str_mv Noncommutative geometry
Artin-Schelter regularity
2-cocycle twists
Zhang twists
topic Noncommutative geometry
Artin-Schelter regularity
2-cocycle twists
Zhang twists
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric variety over k, and we refer to the twists of k[S] as quantum affine toric varieties. We show that every quantum affine toric variety has a “dense quantum torus”, in the sense that it has a localization isomorphic to a quantum torus. We study quantum affine toric varieties and show that many geometric regularity properties of the original toric variety survive the deformation process.
Fil: Rigal, Laurent. Université de Saint-Etienne; Argentina
Fil: Zadunaisky Bustillos, Pablo Mauricio. 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"; Argentina
description We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric variety over k, and we refer to the twists of k[S] as quantum affine toric varieties. We show that every quantum affine toric variety has a “dense quantum torus”, in the sense that it has a localization isomorphic to a quantum torus. We study quantum affine toric varieties and show that many geometric regularity properties of the original toric variety survive the deformation process.
publishDate 2015
dc.date.none.fl_str_mv 2015-08
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/11336/116933
Rigal, Laurent; Zadunaisky Bustillos, Pablo Mauricio; Twisted Semigroup Algebras; Springer; Algebras and Representation Theory; 18; 5; 8-2015; 1155-1186
1386-923X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/116933
identifier_str_mv Rigal, Laurent; Zadunaisky Bustillos, Pablo Mauricio; Twisted Semigroup Algebras; Springer; Algebras and Representation Theory; 18; 5; 8-2015; 1155-1186
1386-923X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10468-015-9525-z
info:eu-repo/semantics/altIdentifier/doi/10.1007%2Fs10468-015-9525-z
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 Springer
publisher.none.fl_str_mv Springer
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 12.982451

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