ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

14. Mathematical Aspects of Computer Science

1991 MS Classification: 46, 19, 81 Kirchberg, Eberhard, Humboldt-Universität zu Berlin Classification of non-simple nuclear C*-algebras There is a generalization KK_{nuc}(X, A, B) of the nuclear KK-functor to the Ψ-equivariant category of C*-algebras A with an upper semicontinuous lattice map Ψ from the open subsets of a T_{0}-space X to the lattice of closed ideals of A (e. g. the 1-1-map Ψ from the open subsets of X := P rim(A) onto the closed ideals of A). For stable separable nuclear A and B, A ⊗ O_{∞} ≅ B ⊗ O_{∞} if and only if (i) X := P rim(A) ≅ P rim(B), (ii) A and B are KK_{nuc}(X, ., .)-equivalent, and (iii) the isomorphism of (i) is given by an isomorphism A ⊗ O_{2} ≅ B ⊗ O_{2}. In some cases one can prove that (i) implies (iii), and that A ≅ A ⊗ O_{∞}. Reference: Kirchberg, E., The classification of purely infinite C*-algebras using Kasparov’s Theory, Fields Inst. Comm. , to appear 1998.