nLab
coadjoint action

Contents

Context

Representation theory

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Definition

For GG a Lie group with Lie algebra 𝔤\mathfrak{g}, the coadjoint action or coadjoint representation of GG is the action/representation on the dual vector space 𝔤 *\mathfrak{g}^* which is dual to the adjoint action of GG on 𝔤\mathfrak{g}.

An orbit of the coadjoint action is accordingly called a coadjoint orbit.

Created on December 30, 2012 at 02:04:57. See the history of this page for a list of all contributions to it.