Examples of such are semisimple Lie algebras, such as su(n) and sl(n,R).
that is invariant under the adjoint action, i.e. where X,Y,Z are elements of the Lie algebra g. A localization/ generalization is the concept of Courant algebroid where the vector space g is replaced by (sections of) a vector bundle.
A big group of examples fits into the category of semisimple Lie algebras, i.e.
Let thus g be a semi-simple Lie algebra with adjoint representation ad, i.e.
Define now the Killing form Due to the Cartan criterion, the Killing form is non-degenerate if and only if the Lie algebra is semisimple.