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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt;3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation>-graded of finite growth over an algebraically closed field of characteristic zero.</p>

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Lie algebras whose derivation algebras are simple

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Jörg Feldvoss,
  • Salvatore Siciliano

摘要

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 \(p>3\) p > 3 or \(\mathbb {Z}\) Z -graded of finite growth over an algebraically closed field of characteristic zero.