Simplicity of crossed products by FC-hypercentral groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912820502724608 |
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| author | Geffen, Shirly Ursu, Dan |
| author_facet | Geffen, Shirly Ursu, Dan |
| contents | In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_λG$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains all virtually nilpotent groups, and in the finitely-generated setting, coincides with the set of groups which have polynomial growth. We further completely characterize the ideal intersection property under the assumption that the group is FC, meaning that every element has a finite conjugacy class. Finally, for minimal actions of arbitrary discrete groups on unital C*-algebras, we are able to characterize when the crossed product $A \rtimes_λG$ is prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07852 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simplicity of crossed products by FC-hypercentral groups Geffen, Shirly Ursu, Dan Operator Algebras 46L55, 47L65 In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_λG$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains all virtually nilpotent groups, and in the finitely-generated setting, coincides with the set of groups which have polynomial growth. We further completely characterize the ideal intersection property under the assumption that the group is FC, meaning that every element has a finite conjugacy class. Finally, for minimal actions of arbitrary discrete groups on unital C*-algebras, we are able to characterize when the crossed product $A \rtimes_λG$ is prime. |
| title | Simplicity of crossed products by FC-hypercentral groups |
| topic | Operator Algebras 46L55, 47L65 |
| url | https://arxiv.org/abs/2304.07852 |