Contents

### Context

#### Representation theory

representation theory

geometric representation theory

## Theorems

#### Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Related topics

Examples

$\infty$-Lie groupoids

$\infty$-Lie groups

$\infty$-Lie algebroids

$\infty$-Lie algebras

# Contents

## Definition

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

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.