Word.ws English Dictionary

Lie group

Lie group noun: any group that is a smooth manifold and whose group operations are differentiable.

Noun

Lie group (plural Lie groups)

  1. Any group that is a smooth manifold and whose group operations are differentiable.
    • 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.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
    • 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

Forms of Lie group

pluralLie groups

Origin of Lie group

Named for Norwegian mathematician Sophus Lie.

Questions about Lie group

What does Lie group mean?
Lie group means any group that is a smooth manifold and whose group operations are differentiable.
What part of speech is Lie group?
Lie group is a noun.
What is the plural of Lie group?
The plural of Lie group is Lie groups.

Words near Lie group in the dictionary

  1. lie detector
  2. lie detectors
  3. lie doggo
  4. lie down
  5. lie down on the job
  6. Lie group
  7. Lie groupoid
  8. Lie groupoids
  9. Lie groups
  10. lie ill in one's mouth
  11. lie in

Source and license

Adapted from Wiktionary: Lie group (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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