Lie ideals in properly infinite C*-algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912427847712768 |
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| author | Thiel, Hannes |
| author_facet | Thiel, Hannes |
| contents | We show that every Lie ideal in a unital, properly infinite C*-algebra is commutator equivalent to a unique two-sided ideal. It follows that the Lie ideal structure of such a C*-algebra is concisely encoded by its lattice of two-sided ideals. This answers a question of Robert in this setting.
We obtain similar structure results for Lie ideals in unital, real rank zero C*-algebras without characters. As an application, we show that every Lie ideal in a von Neumann algebra is related to a unique two-sided ideal, which solves a problem of Brešar, Kissin, and Shulman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lie ideals in properly infinite C*-algebras Thiel, Hannes Operator Algebras Rings and Algebras Primary 46L05, 46L10. Secondary 16W10, 17B60, 47B47 We show that every Lie ideal in a unital, properly infinite C*-algebra is commutator equivalent to a unique two-sided ideal. It follows that the Lie ideal structure of such a C*-algebra is concisely encoded by its lattice of two-sided ideals. This answers a question of Robert in this setting. We obtain similar structure results for Lie ideals in unital, real rank zero C*-algebras without characters. As an application, we show that every Lie ideal in a von Neumann algebra is related to a unique two-sided ideal, which solves a problem of Brešar, Kissin, and Shulman. |
| title | Lie ideals in properly infinite C*-algebras |
| topic | Operator Algebras Rings and Algebras Primary 46L05, 46L10. Secondary 16W10, 17B60, 47B47 |
| url | https://arxiv.org/abs/2412.16087 |