coadjoint
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Coadjoint representation — 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… … Wikipedia
Orbit method — In mathematics, the orbit method (also known as the Kirillov theory, the method of coadjoint orbits and by a few similar names) establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits:… … Wikipedia
Kirillov character formula — In mathematics, for a Lie group G, the Kirillov orbit method gives a heuristic method in representation theory. It connects the Fourier transforms of coadjoint orbits, which lie in the dual space of the Lie algebra of G , to the infinitesimal… … Wikipedia
Moment map — In mathematics, specifically in symplectic geometry, the momentum map (or moment map) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The moment map… … Wikipedia
Symplectomorphism — In mathematics, a symplectomorphism is an isomorphism in the category of symplectic manifolds. Formal definitionSpecifically, let ( M 1, omega;1) and ( M 2, omega;2) be symplectic manifolds. A map : f : M 1 rarr; M 2 is a symplectomorphism if it… … Wikipedia
Jean-Marie Souriau — (born in 1922) is a French mathematician, known for works in symplectic geometry, in which he is one of the pioneers. He has published several works, a treatise on relativity [Sou64b] and a treatise on mechanics: [Sou70] . He has developed the… … Wikipedia
Poisson manifold — In mathematics, a Poisson manifold is a differentiable manifold M such that the algebra of smooth functions over M is equipped with a bilinear map called the Poisson bracket, turning it into a Poisson algebra. Since their introduction by André… … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Reflective subcategory — In mathematics, a subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint. This adjoint is sometimes called a reflector. Dually, A is said to be coreflective in B when the inclusion… … Wikipedia
Kirillov orbit theory — The Kirillov orbit theory or the method of orbits establishes a correspondence between the set of unitary equivalence classes of irreducible representations of a Lie group and the orbits of the action of G on the dual of its Lie algebra… … Wikipedia
