K-theoretic rigidity and slow dimension growth |
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Authors: | Andrew Toms |
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Institution: | 1.Department of Mathematics,Purdue University,West Lafayette,USA |
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Abstract: | Let A be an approximately subhomogeneous (ASH) C∗-algebra with slow dimension growth. We prove that if A is unital and simple, then the Cuntz semigroup of A agrees with that of its tensor product with the Jiang-Su algebra Z\mathcal{Z}. In tandem with a result of W. Winter, this yields the equivalence of Z\mathcal{Z}-stability and slow dimension growth for unital simple ASH algebras. This equivalence has several consequences, including
the following classification theorem: unital ASH algebras which are simple, have slow dimension growth, and in which projections
separate traces are determined up to isomorphism by their graded ordered K-theory, and none of the latter three conditions
can be relaxed in general. |
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