Twisted Semigroup Algebras

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 var...

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Detalles Bibliográficos
Autores: Rigal, Laurent, Zadunaisky Bustillos, Pablo Mauricio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/116933
Acceso en línea:http://hdl.handle.net/11336/116933
Access Level:acceso abierto
Palabra clave:Noncommutative geometry
Artin-Schelter regularity
2-cocycle twists
Zhang twists
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.