Existence and Uniqueness
Cartan subalgebras exist for finite dimensional Lie algebras whenever the base field is infinite. If the field is algebraically closed of characteristic 0 and the algebra is finite dimensional then all Cartan subalgebras are conjugate under automorphisms of the Lie algebra, and in particular are all isomorphic.
Kac–Moody algebras and generalized Kac–Moody algebras also have Cartan subalgebras.
Read more about this topic: Cartan Subalgebra
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