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Funktsional. Anal. i Prilozhen., 2005, Volume 39, Issue 3, Pages 87–91 (Mi faa79)  

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

Translation Invariant Asymptotic Homomorphisms and Extensions of $C^*$-Algebras

V. M. Manuilova, K. Thomsenb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Aarhus, Department of Mathematical Sciences

Abstract: Let $A$ and $B$ be $C^*$-algebras, let $A$ be separable, and let $B$ be $\sigma$-unital and stable. We introduce the notion of translation invariance for asymptotic homomorphisms from $SA=C_0(\mathbb{R})\otimes A$ to $B$ and show that the Connes–Higson construction applied to any extension of $A$ by $B$ is homotopic to a translation invariant asymptotic homomorphism. In the other direction we give a construction which produces extensions of $A$ by $B$ from a translation invariant asymptotic homomorphism. This leads to our main result that the homotopy classes of extensions coincide with the homotopy classes of translation invariant asymptotic homomorphisms.

Keywords: $C^*$-algebra, asymptotic homomorphism, Connes–Higson construction, extension of $C^*$-algebras, homotopy equivalence of extensions, homotopy equivalence of asymptotic homomorphisms

DOI: https://doi.org/10.4213/faa79

Full text: PDF file (183 kB)
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English version:
Functional Analysis and Its Applications, 2005, 39:3, 236–239

Bibliographic databases:

UDC: 517.98
Received: 30.01.2004

Citation: V. M. Manuilov, K. Thomsen, “Translation Invariant Asymptotic Homomorphisms and Extensions of $C^*$-Algebras”, Funktsional. Anal. i Prilozhen., 39:3 (2005), 87–91; Funct. Anal. Appl., 39:3 (2005), 236–239

Citation in format AMSBIB
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\by V.~M.~Manuilov, K.~Thomsen
\paper Translation Invariant Asymptotic Homomorphisms and Extensions of $C^*$-Algebras
\jour Funktsional. Anal. i Prilozhen.
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\vol 39
\issue 3
\pages 87--91
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\transl
\jour Funct. Anal. Appl.
\yr 2005
\vol 39
\issue 3
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    This publication is cited in the following articles:
    1. A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci., 159:5 (2009), 653–751  mathnet  crossref  mathscinet  zmath  elib  elib
    2. A. I. Shtern, “Kazhdan–Milman problem for semisimple compact Lie groups”, Russian Math. Surveys, 62:1 (2007), 113–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Shtern I A., “Continuity Conditions For Finite-Dimensional Locally Bounded Representations of Connected Locally Compact Groups”, Russ. J. Math. Phys., 25:3 (2018), 345–382  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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