Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
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). More recently,the concept of symmetry has been a popular topic of study in the Physics literature under the name of generalized symmetry.
In physics, see local symmetry, global symmetry, asymptotic symmetry spontaneous symmetry breaking.
Historical articles
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)
Hermann Weyl, Symmetry, Journal of the Washington Academy of Sciences 28 6 (1938) 253-271 [jstor:24530200]
On symmetry and introducing the language of homotopy type theory for univalent foundations of mathematics:
Last revised on February 25, 2025 at 07:21:14. See the history of this page for a list of all contributions to it.