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momentum map
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(Definition)
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Let
 be a symplectic manifold,  a Lie group acting on that manifold,
 its Lie algebra, and
 the dual of the Lie algebra. This action induces a map
 where
 is the Lie algebra of vector fields on  , such that
 where  is the flow of  . Then a moment map
 for the action of  is a map such that
Here
 , that is,  is a covector, so we apply it to the vector  and get a scalar function  , and
 is its Hamiltonian vector field.
Generally, the moment maps we are interested in are equivariant with respect to the coadjoint action, that is, they satisfy
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"momentum map" is owned by bwebste.
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(view preamble)
Cross-references: equivariant, Hamiltonian vector field, function, scalar, vector, covector, flow, vector fields, map, induces, action, Lie algebra, manifold, Lie group, symplectic manifold
There is 1 reference to this entry.
This is version 1 of momentum map, born on 2002-12-10.
Object id is 3718, canonical name is MomentumMap.
Accessed 3851 times total.
Classification:
| AMS MSC: | 53D20 (Differential geometry :: Symplectic geometry, contact geometry :: Momentum maps; symplectic reduction) |
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Pending Errata and Addenda
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