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AbstractIf ω is a closed G-invariant 2-form and μ is a moment map, weobtain necessary and sufficient conditions for equivariant prequantizabilitythat can be computed in terms of the moment map μ. Our main result is thatG-equivariant prequantizability is related to the fact that the moment mapμ should be quantized for certain vectors on the Lie algebra of G. Wealso compute the obstructions to lift the action of G to a prequantizationbundle of ω. Our results are valid for any compact and connected Liegroup G.
Forum Mathematicum – de Gruyter
Published: May 1, 2021
Keywords: Equivariant prequantization; equivariant holonomy; moment map; 53D50; 53C29; 58D19
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