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
Famous quotes containing the word program:
“The only thing that was dispensed free to the old New Bedford whalemen was a Bible. A well-known owner of one of that city’s whaling fleets once described the Bible as the best cheap investment a shipowner could make.”
—For the State of Massachusetts, U.S. public relief program (1935-1943)