Universal central extension of the Lie algebra of exact divergence-free vector fields
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.
Authors
- Leonid Ryvkin (ORCID: https://orcid.org/0000-0003-1634-5372)
- Cornelia Vizman (ORCID: https://orcid.org/0000-0002-5551-3984)
- Bas Janssens (ORCID: https://orcid.org/0000-0002-2107-6763)
Institutions
- Université Claude Bernard Lyon 1 (FR)
- West University of Timişoara (RO)
- Institut Camille Jordan (FR)
- Delft University of Technology (NL)
Publication Details
- Journal
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Published
- 2025-08-22
- DOI
- https://doi.org/10.1515/crelle-2025-0053
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Centre National de la Recherche Scientifique
- Université Claude Bernard Lyon 1
- Consiliul National al Cercetarii Stiintifice