Eight-dimensional non completely reducible symplectic Lie algebras

TL;DR

This paper classifies non completely reducible symplectic Lie algebras in dimensions up to 8 and describes symplectic Lie algebras with one-dimensional isotropic ideals, advancing understanding of their structure.

Contribution

It provides a complete classification of non completely reducible symplectic Lie algebras in dimensions up to 8 and characterizes those with one-dimensional isotropic ideals.

Findings

Classification of non completely reducible symplectic Lie algebras in dimension 8

Description of symplectic Lie algebras with one-dimensional isotropic ideals

Structural insights into symplectic Lie algebra reductions

Abstract

A non completely reducible symplectic Lie algebra is a symplectic Lie algebra which cannot be symplectically reduced to the trivial symplectic Lie algebra. Our aim is to provide a complete classification, up to symplectomorphism of non completely reducible symplectic Lie algebras in dimensions $n \leq 8$ and, furthermore, to provide a complete description of symplectic Lie algebras admitting one-dimensional isotropic ideals.