Lie algebras whose derivation algebras are simple
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915123029868544 |
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| author | Feldvoss, Jörg Siciliano, Salvatore |
| author_facet | Feldvoss, Jörg Siciliano, Salvatore |
| contents | It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that have a simple derivation algebra. As an application we classify the Lie algebras that have a complete simple derivation algebra and are either finite-dimensional over an algebraically closed field of prime characteristic $p>3$ or $\mathbb{Z}$-graded of finite growth over an algebraically closed field of characteristic zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_15560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie algebras whose derivation algebras are simple Feldvoss, Jörg Siciliano, Salvatore Rings and Algebras Representation Theory Primary 17B05, Secondary 17B40, 17B56, 17B20, 17B25, 17B50, 17B65, 17B66, 17B68 It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that have a simple derivation algebra. As an application we classify the Lie algebras that have a complete simple derivation algebra and are either finite-dimensional over an algebraically closed field of prime characteristic $p>3$ or $\mathbb{Z}$-graded of finite growth over an algebraically closed field of characteristic zero. |
| title | Lie algebras whose derivation algebras are simple |
| topic | Rings and Algebras Representation Theory Primary 17B05, Secondary 17B40, 17B56, 17B20, 17B25, 17B50, 17B65, 17B66, 17B68 |
| url | https://arxiv.org/abs/2501.15560 |