[en] The role of real Lie algebras in the study of relativistic wave equations of the form (a/sup m/partial/sub m/+ik)u(x) = 0 is considered. To a finite-dimensional equation there corresponds a Lie algebra S containing so(4,C) and a vector operator ]a/sup m/]. The importance of finding all possible real forms of S containing the Lorentz Lie algebra so(3,1) is discussed. This problem is solved in detail for certain ''generic'' cases, namely S = sp(n,C), so(n,C), and sl(n,C). The exceptional algebras G₂, F₄, and E₆ are also considered