# Contents

## Idea

For $G$ a group with action on two objects $X$ and $Y$, there is a canonically induced action on the product $X \times Y$. This is the diagonal action.

## Definition

For every $g\in G$, $g:X\rightarrow X$, $x\mapsto gx$, and $g:Y\rightarrow Y$, $y\mapsto gy$ are both automorphisms, and the maps $g:X\times Y$, $g(x,y)=(gx, gy)$ define the diagonal action of $G$ on $X\times Y$.

Last revised on October 12, 2017 at 01:34:52. See the history of this page for a list of all contributions to it.