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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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_00218693_v284_n1_p415_Farinati |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v284_n1_p415_Farinati |
| Access Level: | acceso abierto |
| Palabra clave: | Duality Hochschild homology and cohomology Localization Smash products |
| Sumario: | 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. |
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