Geodesic Bases for Lie Algebras
arXiv:1312.2186
Abstract
For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existence results in certain cases: unimodular solvable Lie algebras having an abelian nilradical, algebras having an abelian derived algebra, algebras having a codimension one ideal of a particular kind, nonunimodular algebras of dimension $\leq 4$, and unimodular algebras of dimension 5.
18 pages