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

Journal Article (2025)
Author(s)

B. Janssens (TU Delft - Analysis)

Leonid Ryvkin (University of Göttingen, Université Claude Bernard Lyon 1)

Cornelia Vizman (West University of Timisoara (UVT))

Research Group
Analysis
DOI related publication
https://doi.org/10.1515/crelle-2025-0053
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Publication Year
2025
Language
English
Research Group
Analysis
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository as part of the Taverne amendment. More information about this copyright law amendment can be found at https://www.openaccess.nl. Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
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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. De Gruyter 2025.

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