  An explicit construction of a pre-quantum line bundle for the moduli space of
flat G-bundles over a Riemann surface is given, where G is any non-simply
connected compact simple Lie group. This work helps to explain a curious
coincidence previously observed between Toledano-Laredo's work classifying
central extensions of loop groups LG and the author's previous work on the
obstruction to pre-quantization of the moduli space of flat G-bundles.
