Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity)
type: Item
instance of: scholarly article
title: Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity)
zbMATH Open document ID: 0664.46067
DOI: 10.1007/BF01242141
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: The aim of this paper is to show that the cyclic cohomology of an algebra A, associated by the construction given by the first author in the paper ``Non-commutative differential geometry''. Publ. Math., Inst. Hautes Etud. Sci. 62, 41-144 (1985; Zbl 0592.46056) to any homomorphism of the universal algebra qA of the second author in an algebra \(J=L^ p(h^+)\) (the Schatten ideal of p-summable operators on \(h^+)\) equipped with a trace of the suitable domain of \(J^ n\), is obtained by this construction. When A is a \(C^*\)-algebra, so is qA and the authors prove that the notion of positive trace makes sense and it defines a type I or II Fredholm module on A; a notion of positivity for cyclic cocycles is obtained and examplified.
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 55N20
zbMATH DE Number: 4086341
zbMATH Keywords: cyclic cohomology
zbMATH Keywords: universal algebra
zbMATH Keywords: Schatten ideal of p-summable operators
zbMATH Keywords: positive trace
zbMATH Keywords: type I or II Fredholm module
zbMATH Keywords: positivity for cyclic cocycles
author: Alain Connes
author: Joachim Cuntz
MaRDI profile type: Publication
Wikidata QID: Q102144683
cites work: Q4743311
cites work: Non-commutative differential geometry
cites work: Q3317281
cites work: Q3871430
cites work: Q3771069
cites work: A new look at KK-theory
cites work: Q5565478
cites work: Cyclic homology and the Lie algebra homology of matrices
cites work: Tomita's theory of modular Hilbert algebras and its applications
full work available at URL: https://doi.org/10.1007/bf01242141
OpenAlex ID: W1977800563
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description: scientific article; zbMATH DE number 4086341