Premium
Vektorfeldalgebren, Gruppenaktionen und das Keplerproblem
Author(s) -
Hamburger C.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700169
Subject(s) - mathematics , lie group , fundamental vector field , pure mathematics , moment map , symplectic manifold , lie algebra , vector field , diffeomorphism , symplectic geometry , action (physics) , generalized flag variety , algebra over a field , lie conformal algebra , adjoint representation of a lie algebra , physics , geometry , quantum mechanics
We supply an analytic proof of the theorem of Palais about the existence of a Lie group action on a compact manifold M with a Lie algebra of vector fields. Every compact connected integral manifold N of is then diffeomorphic to a homogeneous manifold. In the special case of a Lie algebra of Hamiltonian vector fields, the group action consists of symplectic diffeomorphisms. Applications are the non‐commutative version of the Cauchy initial value problem for Hamilton‐Jacobi systems and of Liouville's theorem. As examples with non‐compact M, we determine group actions for the harmonic oscillator and for Kepler's problem.