# Classification of homomorphisms into simple Z-stable C^*-algebras - Mathematics > Operator Algebras

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Abstract: We classify unital monomorphisms into certain simple Z-stable C^*-algebras upto approximate unitary equivalence. The domain algebra C is allowed to be anyunital separable commutative C^*-algebra, or any unital simple separablenuclear Z-stable C^*-algebra satisfying the UCT such that C\otimes B is oftracial rank zero for a UHF algebra B. The target algebra A is allowed to beany unital simple separable Z-stable C^*-algebra such that A\otimes B hastracial rank zero for a UHF algebra B, or any unital simple separable exactZ-stable C^*-algebra whose projections separate traces and whose extremaltraces are finitely many.

Author: ** Hiroki Matui**

Source: https://arxiv.org/