| Cartan Subalgebra |
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| CATEGORIES ABOUT CARTAN SUBALGEBRA | |
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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. A Cartan subalgebra of a finite dimensional semisimple Lie algebra over an Algebraically Closed Field of characteristic 0 is Abelian and also has the following property of its Eigenspace s of Restricted to diagonalize the representation, and the eigenspace of the zero weight vector is . The non-zero weights are called the Roots , and the corresponding eigenspaces are called ''' Root Spaces ''', and are all 1-dimensional. Kac-Moody Algebra s and Generalized Kac-Moody Algebra s also have Cartan subalgebras. The name is for Élie Cartan . EXAMPLES
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