Universal Central Extension of the Lie Algebra of Hamiltonian Vector Fields

TL;DR

This paper classifies the universal central extension of the Lie algebra of Hamiltonian vector fields and related structures, providing a comprehensive understanding of their central extensions.

Contribution

It determines the universal central extension of Hamiltonian vector fields and classifies extensions of related Lie algebras, advancing the structural understanding of these mathematical objects.

Findings

Universal central extension of Hamiltonian vector fields identified

Classification of central extensions of symplectic and Poisson Lie algebras completed

Extensions of compactly supported versions also classified

Abstract

We determine the universal central extension of the Lie algebra of hamiltonian vector fields, thereby classifying its central extensions. Furthermore, we classify the central extensions of the Lie algebra of symplectic vector fields, of the Poisson Lie algebra, and of its compactly supported version.