Prequantization and Lie brackets

We start by describing the relationship between the classi- cal prequantization condition and the integrability of a certain Lie algebroid associated to the problem and use this to give a global construction of the prequantizing bundle in terms of path spaces (Introduction). Next, we rephrase the problem in terms of groupoids (second section), and then we study the more general problem of prequantizing groupoids endowed with multiplicative 2-forms (the rest of the paper).

2010 Mathematics Subject Classification

Primary 53D50. Secondary 58H05.

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Published 1 January 2004