Takai duality and crossed product hosts in C*-actions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910936905809920 |
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| author | Nakae, Yusuke |
| author_facet | Nakae, Yusuke |
| contents | Crossed product algebras are fundamental in the study of C*-algebras, traditionally under the assumption of continuity of group actions. Recent work by Grundling and Neeb introduced the crossed product host, an analog of the crossed product for a singular action. In this paper, we investigate the structure of the crossed product host and its relation to the conventional crossed product. We examine the validity of Takai-type duality in this setting and establish connections via the Landstad algebra. Additionally, we provide a necessary and sufficient condition for the existence of ground states, and show that for amenable groups, if the full and reduced crossed product hosts exist, then they coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Takai duality and crossed product hosts in C*-actions Nakae, Yusuke Operator Algebras 22D25, 46L55, 47L65, 81R15 Crossed product algebras are fundamental in the study of C*-algebras, traditionally under the assumption of continuity of group actions. Recent work by Grundling and Neeb introduced the crossed product host, an analog of the crossed product for a singular action. In this paper, we investigate the structure of the crossed product host and its relation to the conventional crossed product. We examine the validity of Takai-type duality in this setting and establish connections via the Landstad algebra. Additionally, we provide a necessary and sufficient condition for the existence of ground states, and show that for amenable groups, if the full and reduced crossed product hosts exist, then they coincide. |
| title | Takai duality and crossed product hosts in C*-actions |
| topic | Operator Algebras 22D25, 46L55, 47L65, 81R15 |
| url | https://arxiv.org/abs/2503.09043 |