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2006 Lie Algebra Extensions and Higher Order Cocycles
Karl-Hermann Neeb
J. Geom. Symmetry Phys. 5: 48-74 (2006). DOI: 10.7546/jgsp-5-2006-48-74


In this note we present an abstract approach, based on Lie algebra cohomology, to the Lie algebra extensions associated to symplectic manifolds. We associate to any Lie algebra cocycle of degree at least two an abelian extension by some space a and central extensions of subalgebras analogous to the Lie algebras of symplectic, respectively, hamiltonian vector fields. We even obtain a Poisson bracket on a compatible with the hamiltonian Lie subalgebra. We then describe how this general approach provides a unified treatment of cocycles defined by closed differential forms on Lie algebras of vector fields on possibly infinite-dimensional manifolds.


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Karl-Hermann Neeb. "Lie Algebra Extensions and Higher Order Cocycles." J. Geom. Symmetry Phys. 5 48 - 74, 2006.


Published: 2006
First available in Project Euclid: 20 May 2017

zbMATH: 1105.53064
MathSciNet: MR2269881
Digital Object Identifier: 10.7546/jgsp-5-2006-48-74

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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