Two elements, $X,$ and $Y$ [commute](Commutators.md) if $[X,Y]=0.$ A Lie Algebra commutes if this is true for all of its pairs of elements. i.e. if $\forall X,Y \in \mathfrak{g} \;\;\; [X,Y]=0.$ Such Lie Algebras are also referred to as _[Abelian](Abelian%20algebras) Lie Algebras._ ^7b6f9e #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras