Karoubi's conjecture for the smooth \(K\)-theory
type: Item
instance of: scholarly article
title: Karoubi's conjecture for the smooth \(K\)-theory
zbMATH Open document ID: 1154.19002
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2008-11-28T00:00:00Z
review text: The Karoubi conjecture claims that algebraic and topological \(K\)-theory of stable \(C^*\)-algebras coincide. After being proved [\textit{A. A. Suslin} and \textit{M. Wodzicki}, Ann. Math. (2) 136, No. 1, 51--122 (1992; Zbl 0756.18008)], this conjecture was generalized for wider classes of algebras. The paper under review generalizes this conjecture for quasi-stable Fréchet algebras. A Fréchet algebra is quasi-stable if it is equal to the projective tensor product of the algebra of compact operators by a Fréchet algebra with a properly uniformly bounded approximative unit. In place of the topological \(K\)-theory the authors develop and use smooth \(K\)-theory based on smooth maps.
reviewed by: Vladimir M. Manuilov
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 5374908
zbMATH Keywords: smooth K-theory
zbMATH Keywords: Karoubi conjecture Fréchet algebra
Wikidata QID: Q122969983
author: Hvedri Inassaridze
author: Tamaz Kandelaki
MaRDI profile type: Publication
full work available at URL: j.crma.2008.10.005
OpenAlex ID: W2059255154
cites work: \(K\)-theory of stable generalized operator algebras
cites work: Q3887987
cites work: K-THEORY FOR FRÉCHET ALGEBRAS
cites work: Excision in algebraic \(K\)-theory
cites work: Some relations between higher K-functors
cites work: Excision in cyclic homology and in rational algebraic K-theory
cites work: Q4324347
DOI: 10.1016/J.CRMA.2008.10.005
description: scientific article; zbMATH DE number 5374908