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 a...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00218693_v284_n1_p415_Farinati_oai |
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I28-R145-paper_00218693_v284_n1_p415_Farinati_oai2024-08-16 Farinati, M. 2005 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Algebra 2005;284(1):415-434 Duality Hochschild homology and cohomology Localization Smash products Hochschild duality, localization, and smash 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_00218693_v284_n1_p415_Farinati_oai |
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Universidad de Buenos Aires |
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I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| topic |
Duality Hochschild homology and cohomology Localization Smash products |
| spellingShingle |
Duality Hochschild homology and cohomology Localization Smash products Farinati, M. 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. |
| format |
Artículo Artículo publishedVersion |
| author |
Farinati, M. |
| author_facet |
Farinati, M. |
| author_sort |
Farinati, M. |
| 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 |
http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00218693_v284_n1_p415_Farinati_oai |
| work_keys_str_mv |
AT farinatim hochschilddualitylocalizationandsmashproducts |
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1809356962881601536 |