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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Autores principales:	Carboni, G., Guccione, J.A., Guccione, J.J.
Formato:	Artículo publishedVersion
Publicado:	2010
Materias:	Cyclic homology Hopf crossed products
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00018708_v223_n3_p840_Carboni https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v223_n3_p840_Carboni_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00018708_v223_n3_p840_Carboni_oai
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spelling	I28-R145-paper_00018708_v223_n3_p840_Carboni_oai2024-08-16 Carboni, G. Guccione, J.A. Guccione, J.J. 2010 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00018708_v223_n3_p840_Carboni info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Adv. Math. 2010;223(3):840-872 Cyclic homology Hopf crossed products Cyclic homology of Hopf crossed products info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v223_n3_p840_Carboni_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v223_n3_p840_Carboni_oai
work_keys_str_mv	AT carbonig cyclichomologyofhopfcrossedproducts AT guccioneja cyclichomologyofhopfcrossedproducts AT guccionejj cyclichomologyofhopfcrossedproducts
_version_	1809357179890696192

Cyclic homology of Hopf crossed products

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