Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products

• Autores: Carboni, G.; Guccione, J.A.; Guccione, J.J.; Valqui, C.
• Año de publicación: 2012
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Adv. Math. 2012;231(6):3502-3568
• Materia: Crossed products; Cyclic homology; Hochschild (co)homology
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V. We obtain a mixed complex, simpler than the canonical one, that gives the Hochschild, cyclic, negative and periodic homologies of a crossed product E := A #fV, in the sense of Brzeziński. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A that satisfies suitable hypothesis and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homologies of E relative to K. Then, when E is a cleft braided Hopf crossed product, we obtain a simpler mixed complex, that also gives the Hochschild, cyclic, negative and periodic homologies of E. © 2012 Elsevier Ltd.
Fil:Carboni, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Guccione, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Guccione, J.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.