Split Lie algebra

In the mathematical field of Lie theory, a split Lie algebra is a pair $(\mathfrak{g}, \mathfrak{h})$ where $\mathfrak{g}$ is a Lie algebra and $\mathfrak{h} < \mathfrak{g}$ is a splitting Cartan subalgebra, where "splitting" means that for all $x \in \mathfrak{h}$ , $\operatorname{ad}_{\mathfrak{g}} x$ is triangularizable. If a Lie algebra admits a splitting, it is called a splittable Lie algebra. Note that for reductive Lie algebras, the Cartan subalgebra is required to contain the center.

单词	Split Lie algebra
释义	Split Lie algebra 英语百科 Split Lie algebra In the mathematical field of Lie theory, a split Lie algebra is a pair $(\mathfrak{g}, \mathfrak{h})$ where $\mathfrak{g}$ is a Lie algebra and $\mathfrak{h} < \mathfrak{g}$ is a splitting Cartan subalgebra, where "splitting" means that for all $x \in \mathfrak{h}$ , $\operatorname{ad}_{\mathfrak{g}} x$ is triangularizable. If a Lie algebra admits a splitting, it is called a splittable Lie algebra. Note that for reductive Lie algebras, the Cartan subalgebra is required to contain the center.
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