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arXiv · 1307.8419

A note on extensions of nilpotent algebras of Type 2

Pilar Benito·Daniel de-la-Concepción
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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] (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.

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Pilar Benito, Daniel de-la-Concepción. 2013-07-31. A note on extensions of nilpotent algebras of Type 2. https://arxiv.org/abs/1307.8419

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