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.
Documento: | Artículo |
Título: | Hochschild duality, localization, and smash products |
Autor: | Farinati, M. |
Filiación: | Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, 1428 Buenos Aires, Argentina |
Palabras clave: | Duality; Hochschild homology and cohomology; Localization; Smash products |
Año: | 2005 |
Volumen: | 284 |
Número: | 1 |
Página de inicio: | 415 |
Página de fin: | 434 |
DOI: | http://dx.doi.org/10.1016/j.jalgebra.2004.09.009 |
Título revista: | Journal of Algebra |
Título revista abreviado: | J. Algebra |
ISSN: | 00218693 |
CODEN: | JALGA |
PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v284_n1_p415_Farinati.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v284_n1_p415_Farinati |