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arXiv · 2501.15560

Lie algebras whose derivation algebras are simple

Jörg Feldvoss·Salvatore Siciliano
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Abstract

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.

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Jörg Feldvoss, Salvatore Siciliano. 2025-01-26. Lie algebras whose derivation algebras are simple. https://arxiv.org/abs/2501.15560

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