Translation Invariant Asymptotic Homomorphisms and Extensions of <Emphasis Type="Italic">C</Emphasis>*-Algebras |
| |
Authors: | V M Manuilov K Thomsen |
| |
Institution: | (1) Department of Mathematics and Mechanics, Moscow State University, Moscow, Russia;(2) Institut for Matematiske Fag, Ny Munkegade, Denmark |
| |
Abstract: | Let A and B be C*-algebras, let A be separable, and let B be σ-unital and stable. We introduce the notion of translation invariance for asymptotic homomorphisms from S A = C0(?) ? 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 |
本文献已被 SpringerLink 等数据库收录! |