On Locally Finite Split Lie Triple Systems#

Abstract

Lie triple systems appear as the natural ternary extension of Lie algebras. The classification in the finite-dimensional setup (over an algebraically closed field of characteristic zero) is well-known [Lister, W. G. (1952). A structure theory of Lie triple systems. Trans. Amer. Math. Soc. 72:217–242]. In order to suggest a possible approach to a structure theory of infinite-dimensional Lie triple systems, we introduce and study split and locally finite Lie triple systems, stating that under certain conditions the standard embedding of a split Lie triple system is a split Lie algebra and that the standard embedding of a locally finite Lie triple system is a locally finite Lie algebra. We also give a description of certain locally finite simple split Lie triple systems.