m at h . O A ] 3 1 O ct 2 00 3 SEMI - INVERTIBLE EXTENSIONS AND ASYMPTOTIC HOMOMORPHISMS
نویسندگان
چکیده
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(T) ⊗ A to M (B) that map SA ⊆ C(T) ⊗ A into B.
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