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...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Estado: | Published version |
| Data de publicação: | 2015 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | Inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/116933 |
| Acesso em linha: | http://hdl.handle.net/11336/116933 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Noncommutative geometry Artin-Schelter regularity 2-cocycle twists Zhang twists https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | 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. |
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