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

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

Tooba Feroze1 and Asghar Qadir1,2

1Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of EME College, Peshawar Road, Rawalpindi 46000, Pakistan
2Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 13 March 2009; Revised 30 July 2009; Accepted 20 August 2009

Academic Editor: Tasawar K. Hayat

Copyright © 2009 Tooba Feroze and Asghar Qadir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).