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Equivariant prequantization and the moment map

Equivariant prequantization and the moment map 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Equivariant prequantization and the moment map

Forum Mathematicum , Volume 33 (3): 8 – May 1, 2021

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Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2020-0287
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Forum Mathematicumde Gruyter

Published: May 1, 2021

Keywords: Equivariant prequantization; equivariant holonomy; moment map; 53D50; 53C29; 58D19

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