On the determination of 2step solvable Lie algebra from its weight graph
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 2step solvable. In particular we show that the semidirect product of such a Lie algebra with its torus of derivations cannot be itself 2step solvable.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:math/0011225
 Bibcode:
 2000math.....11225A
 Keywords:

 Mathematics  Rings and Algebras;
 05C99;
 17B30
 EPrint:
 Corrected, minor typographical changes