Universal Central Extension of the Lie Algebra of Hamiltonian Vector Fields

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.

42 pages. Several remarks and examples were added

References in corpus (1)

• Projective unitary representations of infinite dimensional Lie groups

Cited by in corpus (6)

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• Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms
• Stochastic Euler-Poincaré reduction for central extension
• The $L_{\infty }$-algebra of a symplectic manifold