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

Tooba Feroze,Asghar Qadir

doi:10.1155/2009/152698

Abstract

We provide an alternate representation to the result that the Lie algebra of generators of the system ofndifferential 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)″=0issl(n+2,ℝ).

Highlights

The classification of all scalar second-order ordinary differential equations, according to theLie algebra of generators they admit, is complete 1 ; for example, the free particle equation y 0 admits eight Lie symmetries 2, which is the maximum number of symmetries admitted by any second-order differential equation defined on a domain in the plane 1 .This Lie algebra is isomorphic to sl 3, R 3
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
We provide an alternate representation of the symmetry algebra by simple relabelling of indices

Summary

Introduction

The classification of all scalar second-order ordinary differential equations, according to theLie algebra of generators they admit, is complete 1 ; for example, the free particle equation y 0 admits eight Lie symmetries 2 , which is the maximum number of symmetries admitted by any second-order differential equation defined on a domain in the plane 1 .This Lie algebra is isomorphic to sl 3, R 3. Correspondence should be addressed to Tooba Feroze, tferoze@camp.edu.pk 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 . We provide an alternate representation of the symmetry algebra by simple relabelling of indices.

Results

Conclusion