Nuclear dimension and $\mathcal{Z}$-stability of pure C∗-algebras

  title={Nuclear dimension and \$\mathcal\{Z\}\$-stability of pure C∗-algebras},
  author={Wilhelm Winter},
  journal={Inventiones mathematicae},
  • W. Winter
  • Published 1 February 2012
  • Mathematics
  • Inventiones mathematicae
In this article I study a number of topological and algebraic dimension type properties of simple C∗-algebras and their interplay. In particular, a simple C∗-algebra is defined to be (tracially) $(m,\bar{m})$-pure, if it has (strong tracial) m-comparison and is (tracially) $\bar{m}$-almost divisible. These notions are related to each other, and to nuclear dimension.The main result says that if a separable, simple, nonelementary, unital C∗-algebra with locally finite nuclear dimension is $(m… 

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