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

  • Felix Klein, Vergleichende Betrachtungen über neuere geometrische Forschungen (1872)

    translation by M. W. Haskell, A comparative review of recent researches in geometry , trans. M. W. Haskell, Bull. New York Math. Soc. 2, (1892-1893), 215-249. (retyped pdf, retyped pdf, scan of original)

  • Willard Miller, Symmetry Groups and Their Applications, Pure and Applied Mathematics 50 (1972) 16-60 (online pdf)

Last revised on May 12, 2022 at 10:11:09. See the history of this page for a list of all contributions to it.