Moment map ($\mu :M\to {\mathfrak{g}}^{\ast }$)

A moment map assigns to each element of a Lie algebra a Hamiltonian function for its fundamental vector field, and is equivariant for the coadjoint action. For an abelian Lie group, constant shifts are allowed; the numerical scale also depends on the chosen Lie algebra generators and the normalization of the symplectic form.