Hochschild duality, localization, and smash products
- Autores
- Farinati, M.
- Año de publicación
- 2005
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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. - Fuente
- J. Algebra 2005;284(1):415-434
- Materia
-
Duality
Hochschild homology and cohomology
Localization
Smash products - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
.jpg)
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_00218693_v284_n1_p415_Farinati
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Hochschild duality, localization, and smash productsFarinati, M.DualityHochschild homology and cohomologyLocalizationSmash productsIn 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.2005info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_FarinatiJ. Algebra 2005;284(1):415-434reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:43:00Zpaperaa:paper_00218693_v284_n1_p415_FarinatiInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:01.836Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
| dc.title.none.fl_str_mv |
Hochschild duality, localization, and smash products |
| title |
Hochschild duality, localization, and smash products |
| spellingShingle |
Hochschild duality, localization, and smash products Farinati, M. Duality Hochschild homology and cohomology Localization 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 |
| dc.creator.none.fl_str_mv |
Farinati, M. |
| author |
Farinati, M. |
| author_facet |
Farinati, M. |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Duality Hochschild homology and cohomology Localization Smash products |
| topic |
Duality Hochschild homology and cohomology Localization Smash products |
| dc.description.none.fl_txt_mv |
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. |
| 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. |
| publishDate |
2005 |
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2005 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati |
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eng |
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eng |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
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openAccess |
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application/pdf |
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J. Algebra 2005;284(1):415-434 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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