Weakly Hamiltonian action
= Weakly Hamiltonian action
A symplectic <Lie group action> is weakly Hamiltonian when every <fundamental vector field> is a <Hamiltonian vector field>. A <Hamiltonian group action> additionally supplies Hamiltonians as components of an equivariant <moment map>. Constants in the component Hamiltonians do not affect their <vector fields>, but the ability to choose them with the required equivariance is an additional global condition.