Prime and semiprime Lie ideals in C*-algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911247780282368 |
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| author | Gardella, Eusebio Kitamura, Kan Thiel, Hannes |
| author_facet | Gardella, Eusebio Kitamura, Kan Thiel, Hannes |
| contents | Using the theory of Dixmier ideals developed in previous work, we show that every semiprime Lie ideal in a C*-algebra arises as the full normalizer subspace of a semiprime two-sided ideal. This leads to a concise description of all semiprime Lie ideals in terms of semiprime two-sided ideals, and an analogous description of prime Lie ideals in terms of prime two-sided ideals.
For unital C*-algebras without characters, we obtain a natural bijection between (semi)prime two-sided ideals and (semi)prime Lie ideals, and it follows that a Lie ideal is fully noncentral if and only if it is not contained in any prime Lie ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prime and semiprime Lie ideals in C*-algebras Gardella, Eusebio Kitamura, Kan Thiel, Hannes Operator Algebras Rings and Algebras Primary 46L05. Secondary 16N60, 16W10, 17B60 Using the theory of Dixmier ideals developed in previous work, we show that every semiprime Lie ideal in a C*-algebra arises as the full normalizer subspace of a semiprime two-sided ideal. This leads to a concise description of all semiprime Lie ideals in terms of semiprime two-sided ideals, and an analogous description of prime Lie ideals in terms of prime two-sided ideals. For unital C*-algebras without characters, we obtain a natural bijection between (semi)prime two-sided ideals and (semi)prime Lie ideals, and it follows that a Lie ideal is fully noncentral if and only if it is not contained in any prime Lie ideal. |
| title | Prime and semiprime Lie ideals in C*-algebras |
| topic | Operator Algebras Rings and Algebras Primary 46L05. Secondary 16N60, 16W10, 17B60 |
| url | https://arxiv.org/abs/2506.11819 |