Lie Group Valued Moment Maps

  title={Lie Group Valued Moment Maps},
  author={Anton Yu. Alekseev and A. Z. Malkin and ECKHARD MEINRENKEN},
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 × · · · × G. 
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