  We propose the study and description of the structure of complex Lie algebras
with nilradical a nilpotent Lie algebra of type 2 by using
sl2(C)-representation theory. Our results will be applied to review the
classification given in [1] (J. Geometry and Physics, 2011) of the Lie algebras
with nilradical the quasiclassical algebra L5;3. A non-Lie algebra has been
erroneously included in this classification. The 5-dimensional Lie algebra L5;3
is a free nilpotent algebra of type 2 and it is one of two free nilpotent
algebras admitting an invariant metric. According to [, Ok98] quasiclassical
algebras let construct consistent Yang-Mills gauge theories.
