Lie group en · NOUN
Etymology
Named for Norwegian mathematician Sophus Lie.
Meanings
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Any group that is a smooth manifold and whose group operations are differentiable.
As is well known, in finite dimensions each Lie group is, at least locally near the identity, completely described by its Lie algebra.
2009, Boris Khesin, Robert Wendt, The Geometry of Infinite-Dimensional Groups, Springer, page 1:A Lie group is a manifold on which the group manipulations, product and inverse, arc defined. Lie groups play an extremely important role in the theory of fibre bundles and also find vast applications in physics.
2009, Mikio Nakahara, Geometry, Topology and Physics, 2nd edition, Taylor & Francis, page 207:1994, Silvio Levy (translator), Albert S. Schwarz, Topology for Physicists, [1989, A. S. Shvarts, Kvantovaya teoriya polya i topologiya], Springer, 1996, 2nd Printing, page 233, Every connected Lie group is homotopically equivalent to its maximal compact subgroup. This reduces the study of the homotopy and homology of Lie groups to the compact case.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Lie groups | Number=Plur | lexicographic |
Hypernyms
Hyponyms
Relateds
group of Lie type · Lie algebra
Translations (9)
fi Lien ryhmä (analytic group that is also a smooth manifold) · it gruppo di Lie (analytic group that is also a smooth manifold) · ja リー群 (analytic group that is also a smooth manifold) · de Lie-Gruppe (analytic group that is also a smooth manifold) · es grupo de Lie (analytic group that is also a smooth manifold) · da Liegruppe (analytic group that is also a smooth manifold) · fr groupe de Lie (analytic group that is also a smooth manifold) · de Liesche Gruppe (analytic group that is also a smooth manifold) · pl grupa Liego (analytic group that is also a smooth manifold)