Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras

Abstract

We present a classification theorem for a class of unital simple separable amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras by the Elliott invariant. This class of simple $C^{\ast }$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras. Moreover, it contains all unital simple separable amenable $C^{\ast }$-alegbras which satisfy the UCT and have finite rational tracial rank.

272 pages. This revision has 283 pages

References in corpus (1)

• Approximate Homotopy of Homomorphisms from $C(X)$ into a Simple $C^{\ast }$-algebra

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