# nLab effective group action

Contents

this entry is about the concept in group theory; for the concept in quantumfield theory see at effective action functional; for disambiguation see effective action

group theory

### Cohomology and Extensions

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

A group action is effective if no group element other than the neutral element acts trivially on all elements of the space.

## Definition

A group action of a group (group object) $G$ on a set (object) $X$ is effective if $\underset{x \in X}{\forall} g x = x$ implies that $g = e$ is the neutral element.

Beware the similarity to and difference with free action: a free action is effective, but an effective action need not be free.

Last revised on April 14, 2020 at 11:35:14. See the history of this page for a list of all contributions to it.