Year: 2025
Type: article
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: Bas Janssens, Leonid Ryvkin, Cornelia Vizman
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Deutsche Forschungsgemeinschaft, Erwin Schrödinger International Institute for Mathematics and Physics, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Centre National de la Recherche Scientifique, Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii, Université Claude Bernard Lyon 1, Consiliul National al Cercetarii Stiintifice, Institut national des sciences mathématiques et de leurs interactions
OpenAlex ID: W4413445810