Decomposition rank of approximately subhomogeneous C*-algebras

Decomposition rank of subhomogeneous C ∗ -algebras

We analyze the decomposition rank (a notion of covering dimension for nuclear C-algebras introduced by E. Kirchberg and the author) of subhomogeneous C-algebras. In particular we show that a subhomogeneous C-algebra has decomposition rank n if and only if it is recursive subhomogeneous of topological dimension n and that n is determined by the primitive ideal space. As an application, we use re...

On the Classification of Simple Approximately Subhomogeneous C*-algebras Not Necessarily of Real Rank Zero

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their spectrum homeomorphic to the interval [0, 1] or to a finite disjoint union of closed intervals. In particular, a classification of those stably AI algebras which ar...

Decomposition Rank of Z-stable C∗-algebras

We show that C∗-algebras of the form C(X)⊗Z, where X is compact and Hausdorff and Z denotes the Jiang–Su algebra, have decomposition rank at most 2. This amounts to a dimension reduction result for C∗-bundles with sufficiently regular fibres. It establishes an important case of a conjecture on the fine structure of nuclear C∗-algebras of Toms and the second named author, even in a non-simple se...

A Note on Subhomogeneous C-algebras

We show that finitely generated subhomogeneous C∗-algebras have finite decomposition rank. As a consequence, any separable ASH C∗-algebra can be written as an inductive limit of subhomogeneous C∗-algebras each of which has finite decomposition rank. It then follows from work of H. Lin and of the second named author that the class of simple unital ASH algebras which have real rank zero and absor...

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS