Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Coadjoint_representation> ?p ?o. }
Showing items 1 to 15 of
15
with 100 items per page.
- Coadjoint_representation abstract "In mathematics, the coadjoint representation ρ of a Lie group G is the dual of the adjoint representation. Therefore, if g denotes the Lie algebra of G, it is the action of G on the dual space to g. More geometrically, G acts by conjugation on its cotangent space at the identity element e, and this linear representation is ρ. Another geometrical interpretation is as the action by left-translation on the space of right-invariant 1-forms on G.The importance of the coadjoint representation was emphasised by work of Alexandre Kirillov, who showed that for nilpotent Lie groups G a basic role in their representation theory is played by coadjoint orbit. A coadjoint orbit O(x) for x in the dual space g* of g may be defined either extrinsically, as the actual orbit G.x inside g*, or intrinsically as the homogeneous space G/H where H is the stabilizer of x; this distinction is worth making since the embedding of the orbit may be complicated. The coadjoint orbits are all symplectic manifolds with a natural 2-form inherited from g.In the Kirillov method of orbits representations of G are constructed geometrically starting from the coadjoint orbits. In some sense those play a substitute role for the conjugacy classes of G, which again may be complicated, while the orbits are relatively tractable.".
- Coadjoint_representation wikiPageID "3226011".
- Coadjoint_representation wikiPageRevisionID "556677516".
- Coadjoint_representation hasPhotoCollection Coadjoint_representation.
- Coadjoint_representation id "4760".
- Coadjoint_representation title "Coadjoint representation".
- Coadjoint_representation subject Category:Representation_theory_of_Lie_groups.
- Coadjoint_representation subject Category:Symplectic_geometry.
- Coadjoint_representation comment "In mathematics, the coadjoint representation ρ of a Lie group G is the dual of the adjoint representation. Therefore, if g denotes the Lie algebra of G, it is the action of G on the dual space to g. More geometrically, G acts by conjugation on its cotangent space at the identity element e, and this linear representation is ρ.".
- Coadjoint_representation label "Coadjoint representation".
- Coadjoint_representation sameAs m.08_n4z.
- Coadjoint_representation sameAs Q5137654.
- Coadjoint_representation sameAs Q5137654.
- Coadjoint_representation wasDerivedFrom Coadjoint_representation?oldid=556677516.
- Coadjoint_representation isPrimaryTopicOf Coadjoint_representation.