2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149283We present an explicit construction for the central extension of the group $\Map(X, G)$ where $X$ is a compact manifold and $G$ is a Lie group. If $X$ is a complex curve we obtain a simple construction of the extension by the Picard variety $\Pic(X)$. The construction is easily adapted to the extension of $\Aut(E)$, the gauge group of automorphisms of a nontrivial vector bundle $E$.7 pages, harvmac. References addedHigh Energy Physics - TheoryAlgebraic Geometrytext