Say that a separable, unital C *-algebra D â‰‡ C is strongly self-absorbing if there exists an isomorphism Ï• : D â†’ D âŠ— D such that Ï• and id D âŠ— 1 D are approximately unitarily equivalentâ€¦ (More)

We formally introduce the concept of localizing the Elliott conjecture at a given strongly self-absorbing Câˆ—-algebra D; we also explain how the known classification theorems for nuclear Câˆ—-algebrasâ€¦ (More)

Simple, separable, unital, monotracial and nuclear Câˆ—-algebras are shown to have finite nuclear dimension whenever they absorb the Jiangâ€“Su algebra Z tensorially. This completes the proof of theâ€¦ (More)

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 aâ€¦ (More)

We show that, if A is a separable simple unital C-algebra which absorbs the Jiangâ€“Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in theâ€¦ (More)

The radius of comparison is an invariant for unital Câˆ—-algebras which extends the theory of covering dimension to noncommutative spaces. We extend its definition to general Câˆ—-algebras, and give anâ€¦ (More)

We introduce the concept of finitely coloured equivalence for âˆ—-homomorphisms of Câˆ—-algebras, for which unitary equivalence of unital âˆ—-homomorphisms is the 1-coloured case. We use this concept toâ€¦ (More)

We introduce the completely positive rank, a notion of covering dimension for nuclear C *-algebras and analyze some of its properties. The completely positive rank behaves nicely with respect toâ€¦ (More)

We prove the title. This characterizes the Jiangâ€“Su algebra Z as the uniquely determined initial object in the category of strongly self-absorbing C-algebras.

Let X be an infinite, compact, metrizable space of finite covering dimension and Î± : X â†’ X a minimal homeomorphism. We prove that the crossed product C(X) â‹ŠÎ± Z absorbs the Jiang-Su algebraâ€¦ (More)