Symplectic structures on 2-step nilpotent Lie algebras

TL;DR

This paper investigates symplectic structures on 2-step nilpotent Lie algebras, focusing on dimension 8, using subfamily descriptions based on characteristic sequences rather than full classification.

Contribution

It provides a new approach to studying symplectic structures on 2-step nilpotent Lie algebras through subfamily descriptions, especially in dimension 8.

Findings

Characterization of symplectic structures in dimension 8

Description of subfamilies via characteristic sequences

Insights into the complexity of classification beyond dimension 8

Abstract

We study symplectic structures on nilpotent Lie algebras. Since the classification of nilpotent Lie algebras in any dimension seems to be a crazy dream, we approach this study in case of 2-step nilpotent Lie algebras (in this sub-case also, the classification fo the dimension greater than 8 seems very difficult), using not a classification but a description of subfamilies associated with the characteristic sequence. We begin with the dimension $8$, first step where the classification becomes difficult.