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, $(y^a{)}^{″}=0$, is isomorphic to the Lie algebra of the special linear group of order $\left(n+2\right)$, over the real numbers, $sl\left(n+2,ℝ\right)$. 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 $(y^a{)}^{″}=0$ is $sl\left(n+2,ℝ\right)$.