On the k-ary ‎M‎oment Map

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. By considering topological properties of the moment map we are lead to the definition of the abstract moment map. This map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.