Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products

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Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V. We obtain a mixed complex, simpler than the canonical one, that gives the Hochschild, cyclic, negative and periodic homologies of a crossed product E := A #fV, in the sense of Brzezińs...

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Autores principales:	Carboni, G., Guccione, J.A., Guccione, J.J., Valqui, C.
Formato:	Artículo publishedVersion
Publicado:	2012
Materias:	Crossed products Cyclic homology Hochschild (co)homology
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00018708_v231_n6_p3502_Carboni https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v231_n6_p3502_Carboni_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00018708_v231_n6_p3502_Carboni_oai
record_format	dspace
spelling	I28-R145-paper_00018708_v231_n6_p3502_Carboni_oai2024-08-16 Carboni, G. Guccione, J.A. Guccione, J.J. Valqui, C. 2012 Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V. We obtain a mixed complex, simpler than the canonical one, that gives the Hochschild, cyclic, negative and periodic homologies of a crossed product E := A #fV, in the sense of Brzeziński. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A that satisfies suitable hypothesis and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homologies of E relative to K. Then, when E is a cleft braided Hopf crossed product, we obtain a simpler mixed complex, that also gives the Hochschild, cyclic, negative and periodic homologies of E. © 2012 Elsevier Ltd. 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_v231_n6_p3502_Carboni info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Adv. Math. 2012;231(6):3502-3568 Crossed products Cyclic homology Hochschild (co)homology Cyclic homology of Brzeziński's crossed products and of braided 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_v231_n6_p3502_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	Crossed products Cyclic homology Hochschild (co)homology
spellingShingle	Crossed products Cyclic homology Hochschild (co)homology Carboni, G. Guccione, J.A. Guccione, J.J. Valqui, C. Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
topic_facet	Crossed products Cyclic homology Hochschild (co)homology
description	Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V. We obtain a mixed complex, simpler than the canonical one, that gives the Hochschild, cyclic, negative and periodic homologies of a crossed product E := A #fV, in the sense of Brzeziński. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A that satisfies suitable hypothesis and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homologies of E relative to K. Then, when E is a cleft braided Hopf crossed product, we obtain a simpler mixed complex, that also gives the Hochschild, cyclic, negative and periodic homologies of E. © 2012 Elsevier Ltd.
format	Artículo Artículo publishedVersion
author	Carboni, G. Guccione, J.A. Guccione, J.J. Valqui, C.
author_facet	Carboni, G. Guccione, J.A. Guccione, J.J. Valqui, C.
author_sort	Carboni, G.
title	Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
title_short	Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
title_full	Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
title_fullStr	Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
title_full_unstemmed	Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
title_sort	cyclic homology of brzeziński's crossed products and of braided hopf crossed products
publishDate	2012
url	http://hdl.handle.net/20.500.12110/paper_00018708_v231_n6_p3502_Carboni https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v231_n6_p3502_Carboni_oai
work_keys_str_mv	AT carbonig cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts AT guccioneja cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts AT guccionejj cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts AT valquic cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts
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Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products

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