Central localization in Hochschild homology
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.
scientific article; zbMATH DE number 4096372
scientific article