 Automorphism of a Lie algebra

An automorphism of a Lie algebra is an invertible linear map $f:\mathfrak{g}\to \mathfrak{g}$ satisfying $f([X,Y])=[f(X),f(Y)]$.

An automorphism of a Lie algebra is a specific type of isomorphism that is defined within the context of Lie algebras. To be more precise, consider a Lie algebra \( \mathfrak{g} \) over a field (commonly the field of real or complex numbers).