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.
R. Ghanam. B. Basim Mustafa. G. Thompson. "Matrix Representation for Seven-Dimensional Nilpotent Lie Algebras." J. Phys. Math. 7 (1) 1 - 8, 2016. https://doi.org/10.4172/2090-0902.1000155