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

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

2010-02-25

arxiv.org/abs/1002.4790v2

Mathematics

Operator Algebras

Scientific paper

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.

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