Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra
For each nonzero h ∈ F[x], where F is a field, let Ah be the unital associative algebra generated by elements x; y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, containing many well-known algebras which have previously been studied indepe...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/166833 |
| Acceso en línea: | http://hdl.handle.net/11336/166833 |
| Access Level: | acceso abierto |
| Palabra clave: | GERSTENHABER BRACKET HOCHSCHILD COHOMOLOGY ORE EXTENSION WEYL ALGEBRA WITT ALGEBRA https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | For each nonzero h ∈ F[x], where F is a field, let Ah be the unital associative algebra generated by elements x; y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, containing many well-known algebras which have previously been studied independently. In this paper, we give a full description of the Hochschild cohomology HH·(Ah) over a field of an arbitrary characteristic. In case F has a positive characteristic, the center Z(Ah) of Ah is nontrivial and we describe HH·(Ah) as a module over Z.(Ah). The most interesting results occur when F has a characteristic 0. In this case, we describe HH·(Ah) as a module over the Lie algebra HH1(Ah) and find that this action is closely related to the intermediate series modules over the Virasoro algebra. We also determine when HH·(Ah) is a semisimple HH1.Ah/-module. |
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