Hochschild duality, localization, and smash products

In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [Proc. Amer. Math. Soc. 126 (1998) 1345-1348]. More precisely, we consider the class of algebras A such that there exists an invertible bimodule U and an integer number...

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Autor principal: Farinati, Marco Andres
Publicado: 2005
Materias:
Duality
Hochschild homology and cohomology
Localization
Smash products
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v284_n1_p415_Farinati
http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00218693_v284_n1_p415_Farinati
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spelling paper:paper_00218693_v284_n1_p415_Farinati2023-06-08T14:42:22Z Hochschild duality, localization, and smash products Farinati, Marco Andres Duality Hochschild homology and cohomology Localization Smash products In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [Proc. Amer. Math. Soc. 126 (1998) 1345-1348]. More precisely, we consider the class of algebras A such that there exists an invertible bimodule U and an integer number d with the property H• (A, M) ≅ Hd-• (A, U ⊗A M), for all A-bimodules M. We show that this class is closed under localization and under smash products with respect to Hopf algebras satisfying also the duality property. We also illustrate the subtlety on dualities with sma sh products developing in detail the example S(V) # G, the crossed product of the symmetric algebra on a vector space and a finite group acting linearly on V. © 2004 Elsevier Inc. All rights reserved. Fil:Farinati, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v284_n1_p415_Farinati http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Duality
Hochschild homology and cohomology
Localization
Smash products
spellingShingle Duality
Hochschild homology and cohomology
Localization
Smash products
Farinati, Marco Andres
Hochschild duality, localization, and smash products
topic_facet Duality
Hochschild homology and cohomology
Localization
Smash products
description In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [Proc. Amer. Math. Soc. 126 (1998) 1345-1348]. More precisely, we consider the class of algebras A such that there exists an invertible bimodule U and an integer number d with the property H• (A, M) ≅ Hd-• (A, U ⊗A M), for all A-bimodules M. We show that this class is closed under localization and under smash products with respect to Hopf algebras satisfying also the duality property. We also illustrate the subtlety on dualities with sma sh products developing in detail the example S(V) # G, the crossed product of the symmetric algebra on a vector space and a finite group acting linearly on V. © 2004 Elsevier Inc. All rights reserved.
author Farinati, Marco Andres
author_facet Farinati, Marco Andres
author_sort Farinati, Marco Andres
title Hochschild duality, localization, and smash products
title_short Hochschild duality, localization, and smash products
title_full Hochschild duality, localization, and smash products
title_fullStr Hochschild duality, localization, and smash products
title_full_unstemmed Hochschild duality, localization, and smash products
title_sort hochschild duality, localization, and smash products
publishDate 2005
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v284_n1_p415_Farinati
http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati
work_keys_str_mv AT farinatimarcoandres hochschilddualitylocalizationandsmashproducts
_version_ 1768546429025910784

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