On locally finite split Lie triple systems
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. 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.
Antonio J. Calderón Martín < ajesus.calderon@uca.es >
Manuel Forero Piulestán < ForeroManuel@hotmail.com >