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

TL;DR

This paper extends classification methods to nilpotent Lie triple systems, providing algebraic and geometric classifications for systems up to dimension four, enhancing understanding of their structure and variety.

Contribution

It generalizes the Skjelbred Sund method to classify nilpotent Lie triple systems, achieving comprehensive algebraic and geometric classifications up to dimension four.

Findings

Algebraic classification of nilpotent Lie triple systems up to dimension four

Geometric classification of the variety of such systems

Extension of classification methods to triple systems

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.