A vanishing theorem for operations on entire cyclic cohomology
type: Item
instance of: scholarly article
title: A vanishing theorem for operations on entire cyclic cohomology
zbMATH Open document ID: 0815.19004
DOI: 10.1007/BF00961411
author: Masoud Khalkhali
published in: \(K\)-Theory
publication date: 1995-06-13T00:00:00Z
review text: Derivations of an algebra \(A\) act on the Hochschild and cyclic homology of \(A\), and the induced action on periodic cyclic homology is trivial. \textit{E. Getzler} in ``Cartan homotopy formula and the Gauss-Manin connection'' (to appear) extended this action of derivations to a Lie operation of the Hochschild cohomology \(H^* (A,A)\) on the \((b,B)\)- bicomplex of \(A\) and showed that the induced operation on the periodic cyclic homology is trivial. This work is devoted to establish a similar vanishing theorem for entire cyclic cohomology: \[ -\qquad \text{The pairing } H^* (A,A) \otimes HE^* (A) \to HE^* (A) \text{ is trivial.} \] The proof uses a representation theorem of \textit{A. Connes} ``Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules'' [ibid. 1, No. 6, 519-548 (1988; Zbl 0657.46049)].
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 682607
zbMATH Keywords: operations on cyclic homology
zbMATH Keywords: infinite dimensional cycles
zbMATH Keywords: derivations of algebra
zbMATH Keywords: periodic cyclic homology
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: entire cyclic cohomology
reviewed by: Jan Kubarski
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00961411
OpenAlex ID: W1990884819
description: scientific article; zbMATH DE number 682607