Semi-invertible extensions and asymptotic homomorphisms

Details Semi-invertible extensions and asymptotic homomorphisms Semi-invertible extensions and asymptotic homomorphisms

2003-10-31

arxiv.org/abs/math/0310491v1

Mathematics

Operator Algebras

31 pages, LaTeX, XYpic

Scientific paper

We consider the semigroup $Ext(A,B)$ of extensions of a separable C*-algebra $A$ by a stable C*-algebra $B$ modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group $Ext^{-1/2}(A,B)$ of invertible elements (i.e. of semi-invertible extensions). We show that the functor $Ext^{1/2}(A,B)$ is homotopy invariant and that it coincides with the functor of homotopy classes of asymptotic homomorphisms from $C(\mathbb T)\otimes A$ to $M(B)$ that map $SA\subseteq C(\mathbb T)\otimes A$ into $B$.

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