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8. Generators

    1.     A C*-algebra is called singly generated if it contains an element that is not contained in any proper sub-C*-algebra. A C*-algebra is called $\mathcal{Z}$-stable if it absorbs the Jiang-Su algebra tensorially.

      Problem 8.1.

      Which separable, unital, simple C*-algebras are singly generated? Is there a simple, nuclear C*-algebra that is singly generated, yet is not $\mathcal{Z}$-stable? Is single generation connected to the regularity properties coming up in the classification of nuclear, simple C*-algebras?
          It is known that separable, unital C*-algebras are singly generated if they absorb the Jiang-Su algebra.

          Cite this as: AimPL: Set theory and C* algebras, available at http://aimpl.org/settheorycstar.