Cosymplectic and $\alpha$-cosymplectic Lie algebras

TL;DR

This paper provides a complete classification of cosymplectic and $ ext{ extalpha}$-cosymplectic Lie algebras by relating them to symplectic Lie algebras and derivations, including explicit examples and dimension five classifications.

Contribution

It offers a novel characterization of these Lie algebras in terms of symplectic structures and derivations, with new classification results in five dimensions.

Findings

Complete characterization of cosymplectic and $ ext{ extalpha}$-cosymplectic Lie algebras.

Explicit examples illustrating the structures.

Classification of certain Lie algebras in dimension five.

Abstract

We completely characterize cosymplectic and $\alpha$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in dimension five for cosymplectic, $K$-cosymplectic and coK\"ahler Lie algebras.