A note on extensions of nilpotent algebras of Type 2

Abstract: 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 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.