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Lie group valued moment maps. (English) Zbl 0948.53045

Authors’ abstract: “We develop a theory of “quasi”-Hamiltonian \(G\)-spaces for which the moment map takes values in the group \(G\) itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg symplectic cross-section theorem and of convexity properties of the moment map. As an application, we obtain moduli spaces of flat connections on an oriented compact 2-manifold with boundary as quasi-Hamiltonian quotients of the space \(G^2\times\cdots\times G^2\)”.

MSC:

53D20 Momentum maps; symplectic reduction
58D27 Moduli problems for differential geometric structures
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