Abstract
If a Lie group acts on a symplectic manifold preserving the symplectic form, it is possible that each fundamental vector field is the Hamiltonian vector field of a Hamiltonian function called the moment map which was defined in Definition 2.9.
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References
V. Guillemin, S. Sternberg, Convexity properties of the moment mapping I and II. Invent. Math. 67, 491–513 (1982); 77, 533–546 (1984)
V. Guillemin, S. Sternberg, Symplectic Techniques in Physics (Cambridge University Press, Cambridge, 1986)
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Dwivedi, S., Herman, J., Jeffrey, L.C., van den Hurk, T. (2019). Elementary Properties of Moment Maps. In: Hamiltonian Group Actions and Equivariant Cohomology. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-27227-2_4
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DOI: https://doi.org/10.1007/978-3-030-27227-2_4
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