A simple C*-algebra with finite nuclear dimension which is not Z-stable

Abstract

We construct a simple C*-algebra with nuclear dimension zero that is not isomorphic to its tensor product with the Jiang-Su algebra Z, and a hyperfinite II_1 factor not isomorphic to its tensor product with the separable hyperfinite II_1 factor R. The proofs use a weakening of the Continuum Hypothesis.

14 pages

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