Cartan s theorem

In mathematics, there are two basic results in Lie group theory that go by the name Cartan's theorem. They are both named for 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.

See also Cartan's theorems A and B, results of Henri Cartan.

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