The goal of the talk is proving a conjecture of Claude Roger about the universal central extension of the Lie algebra of volume-preserving vector fields. In the beginning we will briefly review the notion of central extensions of Lie algebras and their link to Chevalley-Eilenberg-cohomology. We will then proceed to Roger's conjecture, which lies in the (continuous) infinite-dimensional setting. To solve it we will need a combination of analytical and geometrical methods, and maybe even a bit of representation theory. Based on joint work with Bas Janssens and Cornelia Vizman. -- This seminar is part of the activities of the CIVIS3i programme, funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 101034324.