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arXiv · 2604.27916

Fixed-point-free automorphisms of solvable Lie algebras

Dietrich Burde·Karel Dekimpe
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Abstract

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.

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Dietrich Burde, Karel Dekimpe. 2026-04-30. Fixed-point-free automorphisms of solvable Lie algebras. https://arxiv.org/abs/2604.27916

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