Cyclic homology of Hopf crossed products

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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, G., Guccione, J.A., Guccione, J.J.
Formato:	Artículo publishedVersion
Lenguaje:	Inglés
Publicado:	2010
Materias:	Cyclic homology Hopf crossed products
Acceso en línea:	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	paperaa:paper_00018708_v223_n3_p840_Carboni
record_format	dspace
spelling	paperaa:paper_00018708_v223_n3_p840_Carboni2023-06-12T16:39:29Z Cyclic homology of Hopf crossed products Adv. Math. 2010;223(3):840-872 Carboni, G. Guccione, J.A. Guccione, J.J. 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 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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)
language	Inglés
orig_language_str_mv	eng
topic	Cyclic homology Hopf crossed products
spellingShingle	Cyclic homology Hopf crossed products Carboni, G. Guccione, J.A. Guccione, J.J. 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.
format	Artículo Artículo publishedVersion
author	Carboni, G. Guccione, J.A. Guccione, J.J.
author_facet	Carboni, G. Guccione, J.A. Guccione, J.J.
author_sort	Carboni, G.
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	http://hdl.handle.net/20.500.12110/paper_00018708_v223_n3_p840_Carboni
work_keys_str_mv	AT carbonig cyclichomologyofhopfcrossedproducts AT guccioneja cyclichomologyofhopfcrossedproducts AT guccionejj cyclichomologyofhopfcrossedproducts
_version_	1769810200852692992

Cyclic homology of Hopf crossed products

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