Amenability for unitary groups of C*-algebras
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915040972505088 |
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| author | Alekseev, Vadim Schmidt, Max Thom, Andreas |
| author_facet | Alekseev, Vadim Schmidt, Max Thom, Andreas |
| contents | In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, $\mathcal Z$-stable, UCT C*-algebras with torsionfree K_0 using the progress on the Elliott classification program for nuclear C*-algebras as well as Pestov's study of amenability of gauge groups. Based on work of Kirchberg, we provide a counterexample to a question of Ng, who proposed a different characterization in earlier work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_13181 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Amenability for unitary groups of C*-algebras Alekseev, Vadim Schmidt, Max Thom, Andreas Operator Algebras Group Theory 46L99, 43A07 In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, $\mathcal Z$-stable, UCT C*-algebras with torsionfree K_0 using the progress on the Elliott classification program for nuclear C*-algebras as well as Pestov's study of amenability of gauge groups. Based on work of Kirchberg, we provide a counterexample to a question of Ng, who proposed a different characterization in earlier work. |
| title | Amenability for unitary groups of C*-algebras |
| topic | Operator Algebras Group Theory 46L99, 43A07 |
| url | https://arxiv.org/abs/2305.13181 |