Nilpotent extensions and entire cyclic cohomology
type: Item
instance of: scholarly article
title: Nilpotent extensions and entire cyclic cohomology
zbMATH Open document ID: 0815.19003
DOI: 10.1007/BF00961410
author: Masoud Khalkhali
published in: \(K\)-Theory
publication date: 1995-06-13T00:00:00Z
review text: The author shows that a \(C\)-split of Banach algebras \(0 \to I \to E \to A \to 0\) \((I\) is a nilpotent ideal) induces an isomorphism \(HE^* (A) \to HE^*(E)\) in the entire cyclic cohomology. The proof is based on the following principle [\textit{J. Cuntz} and \textit{D. Quillen}, ``Operators on noncommutative differential forms and cyclic homology'' (to appear), ``Algebra extensions and nonsingularity'' (to appear), ``Cyclic homology and nonsingularity'' (to appear)]: -- under some conditions, a linear map between algebras \(f : A \to B\) induces a functorial ``Connes-Chern character'' map \(Ch(f) : H^* (B) \to H^* (A)\) \((H^*\) is either the periodic or the entire cyclic cohomology functor).
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 46H10
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 18G60
zbMATH DE Number: 682606
zbMATH Keywords: \(X\)-complex
zbMATH Keywords: Fedosov deformation
zbMATH Keywords: Connes-Chern character
zbMATH Keywords: periodic cyclic cohomology
zbMATH Keywords: Banach algebras
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/bf00961410
OpenAlex ID: W2027657039
description: scientific article; zbMATH DE number 682606