Extensions of C*-algebras and translation invariant asymptotic homomorphisms

2003/10/31 by Vladimir Manuilov, V. Manuilov, K. Thomsen +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.OA #msc:19K33

paper · pdf · doi:10.48550/arxiv.math/0310492

22 pages, LaTeX, XYpic

arxiv created 2003/10/31 · arxiv updated 2009/12/01

Abstract

Let A, B be C*-algebras; A separable, B σ-unital and stable. We introduce a notion of translation invariance for asymptotic homomorphisms from SA=C₀(\mathbb R)⊗ 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 out of such 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.

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