Universal central extension of the Lie algebra of exact divergence-free vector fields
Bas Janssens (TU Delft - Analysis)
Leonid Ryvkin (University of Göttingen, Université Claude Bernard Lyon 1)
Cornelia Vizman (West University of Timisoara (UVT))
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Abstract
We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the analysis of a Leibniz algebra that underlies these vector fields. As an application, we construct the universal central extension of the (infinite-dimensional) Lie group of exact divergence-free diffeomorphisms of a compact 3-dimensional manifold.