Automorphisms of real four-dimensional Lie algebras and the invariant characterization of homogeneous 4-spaces

The automorphisms of all four-dimensional, real Lie algebras are presented in a comprehensive way. Their action on the space of 4 × 4, real, symmetric and positive definite matrices defines equivalence classes which are used for the invariant characterization of the four-dimensional homogeneous spaces which possess an invariant basis.