Abstract
If ω is a closed G-invariant 2-form and μ is a moment map, we obtain necessary and sufficient conditions for equivariant prequantizability that can be computed in terms of the moment map μ. Our main result is that G-equivariant prequantizability is related to the fact that the moment map μ should be quantized for certain vectors on the Lie algebra of G. We also compute the obstructions to lift the action of G to a prequantization bundle of ω. Our results are valid for any compact and connected Lie group G.
Funding source: Ministerio de Ciencia, Innovación y Universidades
Award Identifier / Grant number: PGC2018-098321-B-I00
Funding statement: R. Ferreiro Pérez was supported by Ministerio de Ciencia, Innovación y Universidades of Spain under grant PGC2018-098321-B-I00.
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