Classification of homomorphisms into simple Z-stable C^*-algebras

Abstract

We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear Z-stable C^*-algebra satisfying the UCT such that C\otimes B is of tracial rank zero for a UHF algebra B. The target algebra A is allowed to be any unital simple separable Z-stable C^*-algebra such that A\otimes B has tracial rank zero for a UHF algebra B, or any unital simple separable exact Z-stable C^*-algebra whose projections separate traces and whose extremal traces are finitely many.

References in corpus (3)

• Approximate Homotopy of Homomorphisms from $C(X)$ into a Simple $C^{\ast }$-algebra
• Localizing the Elliott conjecture at strongly self-absorbing C*-algebras
• Lifting KK-elements, asymptotical unitary equivalence and classification of simple C*-algebras