Lie–Rinehart and Hochschild cohomology for algebras of differential operators

Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a U-bimodule M and whose second page involves the Lie–Rinehart cohomology of the alge...

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Detalles Bibliográficos
Autores: Kordon, Francisco, Lambre, Thierry
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:11336/157638
Acceso en línea:http://hdl.handle.net/11336/157638
Access Level:acceso abierto
Palabra clave:HOCHSCHILD COHOMOLOGY
LIE-RINEHART ALGEBRAS
ALGEBRAS OF DIFFERENTIAL OPERATORS
HYPERPLANE ARRANGEMENTS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a U-bimodule M and whose second page involves the Lie–Rinehart cohomology of the algebra and the Hochschild cohomology of S with values on M. After giving a convenient description of the involved algebraic structures we use the spectral sequence to compute explicitly the Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of three lines.