Generators in \(\mathcal{Z}\)-stable \(C^{\ast}\)-algebras of real rank zero (Q2697945)
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scientific article; zbMATH DE number 7674621
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generators in \(\mathcal{Z}\)-stable \(C^{\ast}\)-algebras of real rank zero |
scientific article; zbMATH DE number 7674621 |
Statements
Generators in \(\mathcal{Z}\)-stable \(C^{\ast}\)-algebras of real rank zero (English)
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14 April 2023
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Summary: We show that every separable \(C^{\ast}\)-algebra of real rank zero that tensorially absorbs the Jiang-Su algebra contains a dense set of generators. It follows that, in every classifiable, simple, nuclear \(C^{\ast}\)-algebra, a generic element is a generator.
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\(C^{\ast}\)-algebras
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generator rank
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real rank
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generator problem
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single generation
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