On solvable complete symplectic Lie algebras

TL;DR

This paper classifies solvable complete symplectic Lie algebras over the real or complex fields, focusing on those with nilradicals of dimension up to six, providing structural descriptions and classifications.

Contribution

It offers a detailed classification of solvable complete symplectic Lie algebras with small nilradicals, expanding understanding of their structure and symplectic properties.

Findings

Classification of solvable complete symplectic Lie algebras with nilradical dimension ≤ 6

Structural descriptions of these Lie algebras

Identification of key classes supporting symplectic structures

Abstract

In this paper, we are interested in solvable complete Lie algebras, over the field $\K=\R$ or $\mathbb{C}$, which admit a symplectic structure. Specifically, important classes are studied, and a description of complete Lie Algebra with the dimension of nilradical less or equal than six, which supported symplectic structure is given.