Fixed-point-free automorphisms of solvable Lie algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913077119680512 |
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| author | Burde, Dietrich Dekimpe, Karel |
| author_facet | Burde, Dietrich Dekimpe, Karel |
| contents | In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is solvable. We prove that such a Lie algebra must be even strongly unimodular. We find a necessary and sufficient criterion such that a complex almost abelian Lie algebra admits a fixed-point-free automorphism. For complex filiform Lie algebras we show that the existence of a fixed-point-free automorphism is equivalent to not being characteristically nilpotent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27916 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixed-point-free automorphisms of solvable Lie algebras Burde, Dietrich Dekimpe, Karel Rings and Algebras 17B30, 17B08 In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is solvable. We prove that such a Lie algebra must be even strongly unimodular. We find a necessary and sufficient criterion such that a complex almost abelian Lie algebra admits a fixed-point-free automorphism. For complex filiform Lie algebras we show that the existence of a fixed-point-free automorphism is equivalent to not being characteristically nilpotent. |
| title | Fixed-point-free automorphisms of solvable Lie algebras |
| topic | Rings and Algebras 17B30, 17B08 |
| url | https://arxiv.org/abs/2604.27916 |