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

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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Detalles Bibliográficos
Autores principales: Carboni, Graciela, Guccione, Jorge Alberto, Guccione, Juan José
Publicado: 2012
Materias:
Crossed products
Cyclic homology
Hochschild (co)homology
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v231_n6_p3502_Carboni
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 paper:paper_00018708_v231_n6_p3502_Carboni
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spelling paper:paper_00018708_v231_n6_p3502_Carboni2023-06-08T14:21:48Z Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products Carboni, Graciela Guccione, Jorge Alberto Guccione, Juan José 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v231_n6_p3502_Carboni 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)
topic Crossed products
Cyclic homology
Hochschild (co)homology
spellingShingle Crossed products
Cyclic homology
Hochschild (co)homology
Carboni, Graciela
Guccione, Jorge Alberto
Guccione, Juan José
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.
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 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v231_n6_p3502_Carboni
http://hdl.handle.net/20.500.12110/paper_00018708_v231_n6_p3502_Carboni
work_keys_str_mv AT carbonigraciela cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts
AT guccionejorgealberto cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts
AT guccionejuanjose cyclichomologyofbrzezinskiscrossedproductsandofbraidedhopfcrossedproducts
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