Generators · Question 1
Set theory and C-algebras · Historical workshop question
Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code.
Problem statement
Which separable, unital, simple C*-algebras are singly generated? Is there a simple, nuclear C*-algebra that is singly generated, yet is not -stable? Is single generation connected to the regularity properties coming up in the classification of nuclear, simple C*-algebras?
Lean 4
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Background
Question context
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 -stable if it absorbs the Jiang-Su algebra tensorially.
Progress & source assessment
Historical workshop record. Current open/solved status has not been independently reassessed.
Status note in the source
It is known that separable, unital C*-algebras are singly generated if they absorb the Jiang-Su algebra.
- [1]Set theory and C-algebras link
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Discussion
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