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