On Galois descent for Hochschild and cyclic homology
type: Item
instance of: scholarly article
title: On Galois descent for Hochschild and cyclic homology
zbMATH Open document ID: 0816.19003
DOI: 10.1007/BF02564498
author: Martin Lorenz
published in: Commentarii Mathematici Helvetici
publication date: 1995-07-16T00:00:00Z
full work available at URL: https://eudml.org/doc/140349
review text: 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.
reviewed by: Timothy Porter
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 718592
zbMATH Keywords: \(G\)-action
zbMATH Keywords: Hochschild homology
zbMATH Keywords: cyclic homology
zbMATH Keywords: invariants
zbMATH Keywords: algebra of invariants
MaRDI profile type: Publication
OpenAlex ID: W1972807989
description: scientific article; zbMATH DE number 718592