INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
Cyclic homology of Hopf crossed products
GRACIELA CARBONI; JORGE A. GUCCIONE; JUAN J. GUCCIONE
ADVANCES IN MATHEMATICS
ACADEMIC PRESS INC ELSEVIER SCIENCE
Lugar: Amsterdam; Año: 2010 vol. 223 p. 840 - 840
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.