Central localization in Hochschild homology
type: Item
instance of: scholarly article
title: Central localization in Hochschild homology
zbMATH Open document ID: 0669.55001
DOI: 10.1016/0022-4049(89)90022-4
author: Jean-Luc Brylinski
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: For an algebra A with unit and an A-bimodule M, the Hochschild homology groups \(H_ n(A,M)\) are modules over the center Z(A) of A. The author shows that localization of modules over Z(A) commutes with the formation of Hochschild homology [cf. \textit{S. Geller}, \textit{L. Reid} and \textit{C. Weibel}, J. Reine Angew. Math. 393, 39-90 (1989; Zbl 0649.14006)]. A Mayer-Vietoris principle for cyclic homology is deduced [cf. \textit{J. Block}, Harvard thesis (1987) for a general case] and some examples are given. There should be some localization principle unifying central localization and sheaf theory.
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 16Exx
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 4096372
zbMATH Keywords: Hochschild homology groups
zbMATH Keywords: localization of modules
zbMATH Keywords: cyclic homology
reviewed by: Marek Golasiński
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90022-4
OpenAlex ID: W2022048746
cites work: A differential complex for Poisson manifolds
cites work: Q3784990
cites work: The homology of algebras of pseudo-differential symbols and the noncommutative residue
cites work: The cyclic homology and 𝐾-theory of curves
cites work: Sur quelques points d'algèbre homologique
cites work: Q3778132
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description: scientific article; zbMATH DE number 4096372