For a Lie group, an automorphism of the group induces a mapping of the Lie algebra onto itself which preserves the commutation relations. Under an automorphism, the generators are mapped into linear combinations of generators


such that (25.3)

implies (25.4)

Some automorphisms are trivial in the sense that the mapping they induce on the generators is an equivalence:


where R = ei.OaTa is a group element. This is called an inner automorphism. But some of the Lie algebras have non-trivial or outer automorphisms.