Lie algebras whose derivation algebras are simple
J\"org Feldvoss, Salvatore Siciliano

TL;DR
This paper characterizes Lie algebras with simple derivation algebras across arbitrary dimensions and classifies those with complete simple derivation algebras over specific fields and gradings.
Contribution
It extends the classification of Lie algebras with simple derivation algebras to arbitrary dimensions and various field characteristics.
Findings
Characterization of Lie algebras with simple derivation algebras
Classification of Lie algebras with complete simple derivation algebras
Results over fields of prime characteristic and zero with specific gradings
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 or -graded of finite growth over an algebraically closed field of characteristic zero.
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Taxonomy
TopicsAdvanced Topics in Algebra
