Approximately Finite Dimensional C*-algebra - Elliott's Classification Program

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 ρ_A 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.