Examples
In the case of a Hamiltonian action of the circle G = U(1), the Lie algebra dual is naturally identified with R, and the moment map is simply the Hamiltonian function that generates the circle action.
Another classical case occurs when M is the cotangent bundle of R3 and G is the Euclidean group generated by rotations and translations. That is, G is a six-dimensional group, the semidirect product of SO(3) and R3. The six components of the moment map are then the three angular momenta and the three linear momenta.
Read more about this topic: Moment Map
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)