Excision of equivariant cyclic cohomology of topological algebras
type: Item
instance of: scholarly article
title: Excision of equivariant cyclic cohomology of topological algebras
zbMATH Open document ID: 0783.55005
author: Donggeng Gong
published in: Michigan Mathematical Journal
publication date: 1993-06-29T00:00:00Z
review text: The author defines an equivariant cyclic (co)homology theory for Fréchet algebras with continuous action of a compact group. It is defined by a twisted version of the Loday-Quillen bicomplex and is supposed to be the target of a Chern character from equivariant \(K\)- theory. (For example, the equivariant cyclic homology of \(\mathbb{C}\) in degree zero equals the space of class functions on \(G\).) In this context an equivariant Hochschild theory, an equivariant periodic cyclic theory and a Connes-Gysin exact sequence relating equivariant cyclic- and equivariant Hochschild-(co)homology are developed. It is shown that an equivariant \(H\)-unitality condition for a \(G\)-algebra \(J\) (acyclicity of a twisted bar-construction) implies excision, i.e. the existence of a six-term exact sequence for the equivariant periodic cyclic (co)homology groups of the algebras in an equivariant extension with equivariant linear splitting and kernel equal to \(J\). Examples of equivariantly \(H\)- unital algebras are \(G\)-algebras with isometric \(G\)-action (in a strong sense) possessing a uniformly bounded (left) approximate unit as is explained at the end of the paper.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 18G60
zbMATH DE Number: 222031
zbMATH Keywords: equivariant cyclic homology
zbMATH Keywords: equivariant \(K\)-theory
zbMATH Keywords: \(H\)-unitality
zbMATH Keywords: Chern character
zbMATH Keywords: equivariant Hochschild theory
zbMATH Keywords: excision
reviewed by: Michael Puschnigg
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004600
OpenAlex ID: W1996502716
DOI: 10.1307/MMJ/1029004600
description: scientific article; zbMATH DE number 222031