Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra

• Autores: Lopes, Samuel; Solotar, Andrea Leonor
• Año de publicación: 2021
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: GERSTENHABER BRACKET; HOCHSCHILD COHOMOLOGY; ORE EXTENSION; WEYL ALGEBRA; WITT ALGEBRA
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Lopes, Samuel. Universidad de Porto; Portugal
Fil: Solotar, Andrea Leonor. 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