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Cartan subalgebra

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In mathematics, a Cartan subalgebra is a certain kind of subalgebra of a Lie algebra. The subalgebra $\mathfrak{h}$ of a Lie algebra $\mathfrak{g}$ is a Cartan subalgebra if $\mathfrak{h}$ is an abelian subalgebra, with the following property of its adjoint representation: the weight eigenspaces of $\mathfrak{g}$ restricted to $\mathfrak{h}$ diagonalize the representation, and the eigenspace of the zero weight vector is $\mathfrak{h}$ itself.

The name is for Élie Cartan.

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