Relative cyclic homology of square zero extensions

Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of C relative to M. This complex resembles the canonical reduced mixed complex of an augmented alge...

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Autores principales: Guccione, J.A., Guccione, J.J.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00754102_v_n600_p51_Guccione
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00754102_v_n600_p51_Guccione2023-10-03T14:53:56Z Relative cyclic homology of square zero extensions Guccione, J.A. Guccione, J.J. Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of C relative to M. This complex resembles the canonical reduced mixed complex of an augmented algebra. We begin the study of our complex showing that it has a harmonic decomposition like to the one considered by Cuntz and Quillen for the normalized mixed complex of an algebra. We also give new proofs of two theorems of Goodwillie, obtaining a light improvement of one of them. © Walter de Gruyter 2006. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00754102_v_n600_p51_Guccione
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of C relative to M. This complex resembles the canonical reduced mixed complex of an augmented algebra. We begin the study of our complex showing that it has a harmonic decomposition like to the one considered by Cuntz and Quillen for the normalized mixed complex of an algebra. We also give new proofs of two theorems of Goodwillie, obtaining a light improvement of one of them. © Walter de Gruyter 2006.
format JOUR
author Guccione, J.A.
Guccione, J.J.
spellingShingle Guccione, J.A.
Guccione, J.J.
Relative cyclic homology of square zero extensions
author_facet Guccione, J.A.
Guccione, J.J.
author_sort Guccione, J.A.
title Relative cyclic homology of square zero extensions
title_short Relative cyclic homology of square zero extensions
title_full Relative cyclic homology of square zero extensions
title_fullStr Relative cyclic homology of square zero extensions
title_full_unstemmed Relative cyclic homology of square zero extensions
title_sort relative cyclic homology of square zero extensions
url http://hdl.handle.net/20.500.12110/paper_00754102_v_n600_p51_Guccione
work_keys_str_mv AT guccioneja relativecyclichomologyofsquarezeroextensions
AT guccionejj relativecyclichomologyofsquarezeroextensions
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