The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four

Abstract

In this paper we generalize the Skjelbred–Sund method, used to classify nilpotent Lie algebras, in order to classify triple systems with non-zero annihilator. We develop this method with the purpose of classifying nilpotent Lie triple systems, obtaining from it the algebraic classification of the nilpotent Lie triple systems up to dimension four. Additionally, we obtain the geometric classification of the variety of nilpotent Lie triple systems up to dimension four.