Cyclic homology of Hopf crossed products

• Autores: Carboni, G.; Guccione, J.A.; Guccione, J.J.
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Adv. Math. 2010;223(3):840-872
• Materia: Cyclic homology; Hopf crossed products
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

We obtain a mixed complex, simpler than the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E = A #f H, where H is an arbitrary Hopf algebra and f is a convolution invertible cocycle with values in A. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A which is stable under the action of H, and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homology of E relative to K. As an application we obtain two spectral sequences converging to the cyclic homology of E relative to K. The first one works in the general setting and the second one (which generalizes those previously found by several authors) works when f takes its values in K. © 2009 Elsevier Inc. All rights reserved.
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.