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
Lenguaje:	Inglés
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
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paperaa:paper_00018708_v231_n6_p3502_Carboni
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spelling	paperaa:paper_00018708_v231_n6_p3502_Carboni2023-06-12T16:39:30Z Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products Adv. Math. 2012;231(6):3502-3568 Carboni, G. Guccione, J.A. Guccione, J.J. Valqui, C. Crossed products Cyclic homology Hochschild (co)homology 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. 2012 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_v231_n6_p3502_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	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
work_keys_str_mv	AT carbonig cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts AT guccioneja cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts AT guccionejj cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts AT valquic cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts
_version_	1769810056077901824

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

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