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

Bas Janssens; Leonid Ryvkin; Cornelia Vizman

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

Differential Geometry 2025-07-24 v3

Authors: Bas Janssens , Leonid Ryvkin , Cornelia Vizman

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.

Keywords

universal central extension Lie algebra divergence-free vector fields Leibniz algebra Lie group compact 3-dimensional manifold

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@article{arxiv.2409.05182,
  title  = {Universal central extension of the Lie algebra of exact divergence-free vector fields},
  author = {Bas Janssens and Leonid Ryvkin and Cornelia Vizman},
  journal= {arXiv preprint arXiv:2409.05182},
  year   = {2025}
}

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25 pages

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

Abstract

Keywords

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