Ergodic automorphisms on Kirchberg algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908383518392320 |
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| author | Matsumoto, Kengo Sogabe, Taro |
| author_facet | Matsumoto, Kengo Sogabe, Taro |
| contents | Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Kirchberg algebra. In the proof, we give a Pimsner construction realizing many unital subalgebras of a given unital Kirchberg algebra as the fixed point algebras of single automorphisms. Furthermore, for amenable infinite discrete groups, we show that every point-wise outer action on arbitrary unital Kirchberg algebra has an ergodic cocycle perturbation with the help of Gabe--Szabó's theorem and Baum--Connes' conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic automorphisms on Kirchberg algebras Matsumoto, Kengo Sogabe, Taro Operator Algebras Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Kirchberg algebra. In the proof, we give a Pimsner construction realizing many unital subalgebras of a given unital Kirchberg algebra as the fixed point algebras of single automorphisms. Furthermore, for amenable infinite discrete groups, we show that every point-wise outer action on arbitrary unital Kirchberg algebra has an ergodic cocycle perturbation with the help of Gabe--Szabó's theorem and Baum--Connes' conjecture. |
| title | Ergodic automorphisms on Kirchberg algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2505.23168 |