Matrix Representation for Seven-Dimensional Nilpotent Lie Algebras
- *Corresponding Author:
- Ghanam R
Department of Liberal Arts and Sciences
Virginia Commonwealth University in Qatar, Qatar
Tel: +974 4402 0795
E-mail: [email protected]
Received Date: September 15, 2015 Accepted Date: January 12, 2016 Published Date: January 30, 2016
Citation: Ghanam R, Basim Mustafa B, Mustafa MT, Thompson G (2016) Matrix Representation for Seven-Dimensional Nilpotent Lie Algebras. J Phys Math 7:155. doi:10.4172/2090-0902.1000155
Copyright: © 2016 Ghanam R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
This paper is concerned with finding linear representations for seven-dimensional real, indecomposable nilpotent Lie algebras. We consider the first 39 algebras presented in Gong’s classification which was based on the upper central series dimensions. For each algebra, we give a corresponding matrix Lie group, a representation of the Lie algebra in terms of left-invariant vector field and left-invariant one forms.