On the $k$-ary ‎M‎oment Map

Subject Areas : International Journal of Industrial Mathematics

محمد دارا ¹ , اکبر دهقان نژاد ²

1 - School of Mathematics, Iran University of Science and Technology, Tehran, Iran.
2 - School of Mathematics, Iran University of Science and Technology, Tehran, Iran.

Received: 2019-11-05 Accepted : 2020-10-07 Published : 2021-01-01

Keywords: reduction, Lie algebra, K-ary moment map, Moment map, Hamiltonian system,

Abstract :

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment 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.

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