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arXiv · 1402.2212

Inner derivations of exceptional Lie algebras in prime characteristic

Pablo Alberca-Bjerregaard·Dolores Martín-Barquero·Cándido Martín-González
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Abstract

It is well-known that every derivation of a semisimple Lie algebra $L$ over an algebraically closed field $F$ with characteristic zero is inner. The aim of this paper is to show what happens if the characteristic of $F$ is prime with $L$ an exceptional Lie algebra. We prove that if $L$ is a Chevalley Lie algebra of type $\{G_2,F_4,E_6,E_7,E_8\}$ over a field of characteristic $p$ then the derivations of $L$ are inner except in the cases $G_2$ with $p=2$, $E_6$ with $p=3$ and $E_7$ with $p=2$.

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Pablo Alberca-Bjerregaard, Dolores Martín-Barquero, Cándido Martín-González. 2014-02-10. Inner derivations of exceptional Lie algebras in prime characteristic. https://arxiv.org/abs/1402.2212

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