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:
“Resorts advertised for waitresses, specifying that they must appear in short clothes or no engagement. Below a Gospel Guide column headed, Where our Local Divines Will Hang Out Tomorrow, was an account of spirited gun play at the Bon Ton. In Jeff Winneys California Concert Hall, patrons bucked the tiger under the watchful eye of Kitty Crawhurst, popular lady gambler.”
—Administration in the State of Colo, U.S. public relief program (1935-1943)