The paper by David Fisher, Robert Gray and Peter Hydon, entitled “Automorphisms of real Lie algebras of dimension five or less” has been accepted for publication in the Journal of Physics A. The main result of the paper is a formulation and proof of a Lie algebra version of the Krull-Schmidt Theorem. This theorem leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. It is illustrated by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. A link to the final form preprint is here.