Cyclic homology of Hopf crossed products

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 re...

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Detalles Bibliográficos
Autores principales: Carboni, Graciela, Guccione, Jorge Alberto, Guccione, Juan José
Publicado: 2010
Materias:
Cyclic homology
Hopf crossed products
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v223_n3_p840_Carboni
http://hdl.handle.net/20.500.12110/paper_00018708_v223_n3_p840_Carboni
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00018708_v223_n3_p840_Carboni
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spelling paper:paper_00018708_v223_n3_p840_Carboni2023-06-08T14:21:46Z Cyclic homology of Hopf crossed products Carboni, Graciela Guccione, Jorge Alberto Guccione, Juan José Cyclic homology Hopf crossed products 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v223_n3_p840_Carboni http://hdl.handle.net/20.500.12110/paper_00018708_v223_n3_p840_Carboni
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cyclic homology
Hopf crossed products
spellingShingle Cyclic homology
Hopf crossed products
Carboni, Graciela
Guccione, Jorge Alberto
Guccione, Juan José
Cyclic homology of Hopf crossed products
topic_facet Cyclic homology
Hopf crossed products
description 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.
author Carboni, Graciela
Guccione, Jorge Alberto
Guccione, Juan José
author_facet Carboni, Graciela
Guccione, Jorge Alberto
Guccione, Juan José
author_sort Carboni, Graciela
title Cyclic homology of Hopf crossed products
title_short Cyclic homology of Hopf crossed products
title_full Cyclic homology of Hopf crossed products
title_fullStr Cyclic homology of Hopf crossed products
title_full_unstemmed Cyclic homology of Hopf crossed products
title_sort cyclic homology of hopf crossed products
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v223_n3_p840_Carboni
http://hdl.handle.net/20.500.12110/paper_00018708_v223_n3_p840_Carboni
work_keys_str_mv AT carbonigraciela cyclichomologyofhopfcrossedproducts
AT guccionejorgealberto cyclichomologyofhopfcrossedproducts
AT guccionejuanjose cyclichomologyofhopfcrossedproducts
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