Lie algebras whose derivation algebras are simple

2025/01/26 by Jörg Feldvoss, Salvatore Siciliano, Feldvoss, Jörg +1
Mathematics · #17B20 #17B25 #17B50 #17B56 #17B65 #17B66 #17B68 #Advanced Topics in Algebra #FOS: Mathematics #Primary 17B05 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 17B40

paper · pdf · doi:10.48550/arxiv.2501.15560

openalex publication_date 2025/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℤ-graded of finite growth over an algebraically closed field of characteristic zero.

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• Simple Lie algebras of small characteristic VI. Completion of the classification
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