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Central Extensions of Loop Groups and Obstruction to Pre-Quantization

Open Access article
 Printed: Mar 2013
  • Derek Krepski,
    Department of Mathematics and Statistics, McMaster University, Hamilton, ON
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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.
Keywords: loop group, central extension, prequantization loop group, central extension, prequantization
MSC Classifications: 53D, 22E show english descriptions unknown classification 53D
unknown classification 22E
53D - unknown classification 53D
22E - unknown classification 22E

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