A Note on the Automorphism Groups of Lie Module Triple Systems

Abstract

Using representation theory and well-known facts about automorphism groups of reductive Lie algebras, the automorphism group of a basic Lie module triple system $(M,\{ ,,\} ,\mathcal {L},b,\phi )$ over an algebraically closed field of characteristic zero is related to the automorphism group of the Lie algebra $\mathcal {L}$, the automorphism group of the standard embedding $\mathcal {S}$ of $(M,\{ ,,\} )$, and the automorphism group of the split null extension $\mathcal {S}$ of $\mathcal {L}$ by $M$.