Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 152698, 3 pages
doi:10.1155/2009/152698

Another Representation for the Maximal Lie Algebra of sl(n+2,ℝ) in Terms of Operators

Abstract

We provide an alternate representation to the result that the Lie algebra of generators of the system of n differential equations, (ya)″=0, is isomorphic to the Lie algebra of the special linear group of order (n+2), over the real numbers, sl(n+2,ℝ). In this paper, we provide an alternate representation of the symmetry algebra by simple relabelling of indices. This provides one more proof of the result that the symmetry algebra of (ya)″=0 is sl(n+2,ℝ).