Cyclic homology of Hopf crossed products |
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Authors: | Graciela Carboni Jorge A Guccione Juan J Guccione |
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Institution: | a Cíclo Básico Común, Departamento de Ciencias Exactas, Pabellón 3 - Ciudad Universitaria, (1428) Buenos Aires, Argentina b Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón 1 - Ciudad Universitaria, (1428) Buenos Aires, Argentina |
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Abstract: | We obtain a mixed complex, simpler than the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E=A#fH, 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. |
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Keywords: | primary 16E40 secondary 16W30 |
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