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Any group that is a smooth manifold and whose group operations are differentiable.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences, topology
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named for Norwegian mathematician Sophus Lie.
Across languages
Translations
9 source translations are retained for this English entry.
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Danish:
Liegruppe
— analytic group that is also a smooth manifold
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Finnish:
Lien ryhmä
— analytic group that is also a smooth manifold
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French:
groupe de Lie
— analytic group that is also a smooth manifold
-
German:
Lie-Gruppe
— analytic group that is also a smooth manifold
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German:
Liesche Gruppe
— analytic group that is also a smooth manifold
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Italian:
gruppo di Lie
— analytic group that is also a smooth manifold
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Japanese:
リー群
(rīgun)
— analytic group that is also a smooth manifold
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Polish:
grupa Liego
— analytic group that is also a smooth manifold
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Spanish:
grupo de Lie
— analytic group that is also a smooth manifold
