Central extensions of Lie algebras of symplectic and divergence free vector fields

TL;DR

This paper reviews central extensions of Lie algebras related to symplectic and divergence free vector fields, discussing their universal properties and group-level integrability.

Contribution

It provides a comparative analysis of central extensions in symplectic and divergence free vector field Lie algebras, highlighting universal extensions and integrability aspects.

Findings

Comparison of central extensions between symplectic and divergence free Lie algebras

Discussion on universal central extensions and their properties

Analysis of integrability to the group level for these Lie algebras

Abstract

In this review paper, we present several results on central extensions of the Lie algebra of symplectic (Hamiltonian) vector fields, and compare them to similar results for the Lie algebra of (exact) divergence free vector fields. In particular, we comment on universal central extensions and integrability to the group level.