K-theoretic rigidity and slow dimension growth
A Toms�- Inventiones mathematicae, 2011 - Springer
Inventiones mathematicae, 2011•Springer
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. In tandem with a result of W. Winter,
this yields the equivalence of 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�…
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. In tandem with a result of W. Winter,
this yields the equivalence of 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�…
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 . In tandem with a result of W. Winter, this yields the equivalence of -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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