Inner derivations of exceptional Lie algebras in prime characteristic

2014/02/10 by Pablo Alberca-Bjerregaard, Alberca-Bjerregaard, Pablo, Dolores Martín-Barquero +3
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1402.2212

openalex publication_date 2014/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \G₂,F₄,E₆,E₇,E₈\ over a field of characteristic p then the derivations of L are inner except in the cases G₂ with p=2, E₆ with p=3 and E₇ with p=2.

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