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- Cartan's_theorem abstract "In mathematics, three results in Lie group theory are called Cartan's theorem, named after Élie Cartan:1. The theorem that for a Lie group G, any closed subgroup is a Lie subgroup.2. A theorem on highest weight vectors in the representation theory of a semisimple Lie group.3. The equivalence between the category of simply connected real Lie groups and finite-dimensional real Lie algebras is called usually (in the literature of the second half of 20th century) Cartan's or Cartan-Lie theorem as it is proved by Élie Cartan whereas S. Lie has proved earlier just the infinitesimal version (local solvability of Maurer-Cartan equations (see Maurer-Cartan form) or the equivalence between the finite-dimensional Lie algebras and the category of local Lie groups). Lie listed his results as 3 direct and 3 converse theorems, the infinitesimal variant of Cartan's theorem was essentially his 3rd converse theorem, hence Serre has called it in an influential book, the "third Lie theorem", the name which is historically somewhat misleading, but more often used in the recent decade Template:As of? in the connection to many generalizations.See also Cartan's theorems A and B, results of Henri Cartan, and Cartan's lemma for various other results attributed to Élie and Henri Cartan.".
- Cartan's_theorem wikiPageID "621655".
- Cartan's_theorem wikiPageRevisionID "598770420".
- Cartan's_theorem hasPhotoCollection Cartan's_theorem.
- Cartan's_theorem subject Category:Lie_groups.
- Cartan's_theorem subject Category:Theorems_in_abstract_algebra.
- Cartan's_theorem type Abstraction100002137.
- Cartan's_theorem type Communication100033020.
- Cartan's_theorem type Group100031264.
- Cartan's_theorem type LieGroups.
- Cartan's_theorem type Message106598915.
- Cartan's_theorem type Proposition106750804.
- Cartan's_theorem type Statement106722453.
- Cartan's_theorem type Theorem106752293.
- Cartan's_theorem type TheoremsInAbstractAlgebra.
- Cartan's_theorem type TheoremsInAlgebra.
- Cartan's_theorem comment "In mathematics, three results in Lie group theory are called Cartan's theorem, named after Élie Cartan:1. The theorem that for a Lie group G, any closed subgroup is a Lie subgroup.2. A theorem on highest weight vectors in the representation theory of a semisimple Lie group.3.".
- Cartan's_theorem label "Cartan's theorem".
- Cartan's_theorem label "Teorema de Cartan".
- Cartan's_theorem label "Théorème de Cartan".
- Cartan's_theorem sameAs Teorema_de_Cartan.
- Cartan's_theorem sameAs Théorème_de_Cartan.
- Cartan's_theorem sameAs m.02xl2p.
- Cartan's_theorem sameAs Q3527031.
- Cartan's_theorem sameAs Q3527031.
- Cartan's_theorem sameAs Cartan's_theorem.
- Cartan's_theorem wasDerivedFrom Cartan's_theorem?oldid=598770420.
- Cartan's_theorem isPrimaryTopicOf Cartan's_theorem.