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# Central Extensions of Loop Groups and Obstruction to Pre-Quantization

Published:2011-06-29
Printed: Mar 2013
• Derek Krepski,
Department of Mathematics and Statistics, McMaster University, Hamilton, ON
 Format: LaTeX MathJax PDF

## Abstract

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
 MSC Classifications: 53D - unknown classification 53D22E - unknown classification 22E

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