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On the determination of 2-step solvable Lie algebra from its weight graph

Jose Maria Ancochea·Otto Rutwig Campoamor
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Abstract

By using the concept of weight graph associated to certain nilpotent Lie algebras $\frak{g}$, we find necessary and sufficient conditions for a semidirect product $\frak{g}\oplus T_{i}$, where $T_{i}<T$ is a subalgebra of a maximal torus of derivations $T$ of $\frak{g}$ which induces a decomposition of $\frak{g}$ into one dimensional weight spaces, to be 2-step solvable. In particular we show that the semidirect product of such a Lie algebra with its torus of derivations cannot be itself 2-step solvable.

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Jose Maria Ancochea, Otto Rutwig Campoamor. 2001-01-12. On the determination of 2-step solvable Lie algebra from its weight graph. https://arxiv.org/abs/math/0011225

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