Recasting the Elliott Conjecture

@inproceedings{Toms2006RecastingTE,
  title={Recasting the Elliott Conjecture},
  author={Andrew S. Toms},
  year={2006}
}
Let A be a simple, unital, finite, and exact C∗-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomorphism, and prove the conjecture in several cases. In these same cases — Z-stable algebras all — we prove that the Elliott conjecture in its strongest form is equivalent to a… CONTINUE READING
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