Central localization in Hochschild homology

Abstract

If A is an algebra with unit, M an A-bimodule, the Hochschild homology groups H i ( A, M) are modules over the center Z( A). We show that these homology groups behave well with respect to localization in the commutative ring Z( A). We deduce a Mayer-Vietoris principle, and give some examples (commutative algebras, enveloping algebras, crossed–product algebras).