Cartan's theorem

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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.

[edit] References

• Helgason, Sigurdur (2001), Differential geometry, Lie groups, and symmetric spaces, Graduate Studies in Mathematics, 34, Providence, R.I.: American Mathematical Society, MR1834454, ISBN 978-0-8218-2848-9