2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60858We give a characterisation of central extensions of a Lie group G by the non-zero complex numbers in terms of a differential two-form on G and a differential one-form on GxG. This is applied to the case of the central extension of the loop group.Conference talk at the National Research Symposium on Geometric Analysis and Applications at the Centre for Mathematics and its ApplicationsDifferential Geometry22E67Yet another construction of the central extension of the loop grouptext