A classification of finite simple amenable Z-stable C*-algebras, II, --C*-algebras with rational generalized tracial rank one

Abstract

A classification theorem is obtained for a class of unital simple separable amenable Z-stable C*-algebras which exhausts all possible values of the Elliott invariant for unital stably finite simple separable amenable Z-stable C*-algebras. Moreover, it contains all unital simple separable amenable C*-algebras which satisfy the UCT and have finite rational tracial rank

arXiv commentThis is a publication version of the last part of the original preprint (A classification of finite simple amenable Z-stable C*-algebras, arXiv:1501.00135). Appeared in C. R. Math. Acad. Sci. Soc. R. Canada

References in corpus (2)

• A simple C*-algebra with a finite and an infinite projection
• Approximate Homotopy of Homomorphisms from $C(X)$ into a Simple $C^{\ast }$-algebra

Cited by in corpus (6)

• Nuclear dimension of simple C*-algebras
• On classification of non-unital amenable simple C*-algebras, III, the range and the reduction
• Nuclear dimension of crossed products associated to partial dynamical systems
• Constructing Menger manifold C*-diagonals in classifiable C*-algebras
• A geometric Elliott invariant and noncommutative rigidity of mapping tori
• The UCT problem for nuclear $C^{\ast }$-algebras