Resumen de Extensions of C* - algebras and translation invariant asymptotic homomorphisms
Vladimir Manuilov, Klaus Thomsen
Let A, B be C* algebras; A separable, B [O]-unital and stable. We introduce a notion of translation invariance for asymptotic homomorphisms from SA = C0(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 directionwe 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.
