On Galois descent for Hochschild and cyclic homology
Let \(G\) be a finite group acting on an algebra \(S\) over some commutative ring \(k\), then \(G\) acts on both Hochschild homology \(HH_ * (S)\) and on the cyclic homology \(HC_ * (S)\) of \(S\). One can thus compare the invariants of these homologies under the \(G\)-action with the corresponding homology of \(S^ G\), the algebra of invariants. This paper proves that if the action of \(G\) on the centre of \(S\) is Galois then the obvious induction map from \(HH_ * (S^ G)\) to \(HH_ * (S)^ G\) is an isomorphism and that if in addition the order of \(G\) is invertible in \(k\), a similar result holds for cyclic homology.
scientific article; zbMATH DE number 718592