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

2024/09/08 by Bas Janssens, Janssens, Bas, Leonid Ryvkin +3 · 1 citation
Mathematics · #17B56 #17B66 #58D05 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2409.05182

openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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