Universal central extension of the Lie algebra of exact divergence-free vector fields

Bas Janssens; Leonid Ryvkin; Cornelia Vizman

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arXiv · 2409.05182

Universal central extension of the Lie algebra of exact divergence-free vector fields

Bas Janssens·Leonid Ryvkin·Cornelia Vizman

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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.

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Bas Janssens, Leonid Ryvkin, Cornelia Vizman. 2024-09-08. Universal central extension of the Lie algebra of exact divergence-free vector fields. https://arxiv.org/abs/2409.05182

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