If a [[Lie algebra homomorphisms]], $\phi,$ is also one-to-one and onto, then $\phi$ is also a [Lie algebra](Lie%20algebras.md) [isomorphism](Isomorphisms.md). In addition, a Lie Algebra that is isomorphic with itself is called a _Lie Algebra automorphism_. %%One-to-one and onto need to be defined but that definition should simply be inherited from the general definition of an isomorphism%% #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras