Simple Amenable C∗-algebras With a Unique Tracial State
نویسنده
چکیده
Let A be a unital separable amenable quasidiagonal simple C∗-algebra with real rank zero, stable rank one, weakly unperforated K0(A) and with a unique tracial state. We show that A must have tracial rank zero. Suppose also that A satisfies the Universal Coefficient Theorem. Then A can be classified by its (ordered) K-theory up to isomorphism. In particular, A must be a simple AH-algebra with no dimension growth and with real rank zero. As consequence, if A is a unital separable amenable quasidiagonal and approximately divisible simple C∗-algebra with a unqiue tracial state, then A has tracial rank zero.
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