Metric Symplectic Lie Algebras

TL;DR

This paper classifies metric symplectic Lie algebras by representing them as quadratic extensions, providing a standard model, and describing their equivalence classes through quadratic cohomology, including complete classifications in special cases.

Contribution

It introduces a standard model for metric symplectic Lie algebras and develops a scheme to classify their isomorphism classes using quadratic cohomology.

Findings

Standard model for metric symplectic Lie algebras

Classification scheme for isomorphism classes

Complete list of such Lie algebras in special cases

Abstract

Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the isomorphism classes of metric symplectic Lie algebras and give a complete list of all these Lie algebras in special cases.