Elliott's Classification Program
It was proposed by Elliott that other classes of C*-algebras may be classifiable by K-theoretic invariants. For a C*-algebra A, the Elliott invariant is defined to be
where T+(A) is the tracial positivel linear functionals in the weak-* topology, and ρA is the natural pairing between T+(A) and K0(A).
The original conjecture by Elliott stated that the Elliott invariant classifies simple unital separable nuclear C*-algebras.
In the literature one can find several conjectures of Elliott type, with corresponding modified/refined Elliott invariants.
Read more about this topic: Approximately Finite Dimensional C*-algebra
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