nLab
diagonal action

Contents

Idea

For GG a group with action on two objects XX and YY, there is a canonically induced action on the product X×YX \times Y. This is the diagonal action.

Definition

For every gGg\in G, g:XXg:X\rightarrow X, xgxx\mapsto gx, and g:YYg:Y\rightarrow Y, ygyy\mapsto gy are both automorphisms, and the maps g:X×Yg:X\times Y, g(x,y)=(gx,gy)g(x,y)=(gx, gy) define the diagonal action of GG on X×YX\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.