
It is well known that we have three momentum map theories, or at least three natural \(G\)-spaces which serve as targets for moment maps: \(\mathfrak{g}^*\) for the classical Hamiltonian theory, \(G\) for the \(q\)-Hamiltonian theory and \(G_\mathbb{C}/G\) representing the Poisson or \(Y\)-valued theory. In the paper under review the author brings these theories into a unified framework. He shows that given a symmetric pair \((H,G)\) with a special pairing on the Lie algebra of \(H\), one may construct an equivariantly closed \(3\)-form on \(P=H/G\) and a momentum map theory. As particular cases one refines the momentum theories mentioned above.
symmetric pair, \(G\)-spaces, Momentum maps; symplectic reduction, Lie algebras of Lie groups, forms, momentum maps
symmetric pair, \(G\)-spaces, Momentum maps; symplectic reduction, Lie algebras of Lie groups, forms, momentum maps
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