Representation coadjointe

The representation coadjointe $\backslash \; rho$ of a Groupe of Dregs G is the natural action of G on the dual one of sound Algèbre of Dregs $\backslash \; mathfrak\; \{G\}$. More explicitly, G acts by conjugation on its space cotangent in the neutral element E and this linear Représentation is given by the morphism of group of Dregs:

$\backslash rho:G\; \backslash \; rightarrow\; End\; (\backslash \; mathfrak\; \{G\}\; ^*)$

Geometrical interpretation: this action is seen like the action by translation on the left on the space of the invariant forms on the right on G .

The orbit coadjointe plays a central role in the theory of the representation.

The orbits coadjointes are symplectic varieties.

See too

• Hamiltonian Action

• Group of Dregs

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