nLab symmetry

Contents

Contents

Idea

A symmetry is (in most classical situations) invariance under a group action, or infinitesimally, invariance under a Lie algebra action. Indeed, historically the mathematical term “group” is a contraction of group of symmetries (e.g. Klein 1872).

In physics, see local symmetry, global symmetry, spontaneous symmetry breaking.

Examples

References

Historical articles

On transformation groups:

On symmetry and introducing the language of homotopy type theory for univalent foundations of mathematics:

Last revised on July 13, 2022 at 14:27:11. See the history of this page for a list of all contributions to it.