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arXiv · 1302.2751

On the existence of orthonormal geodesic bases for Lie algebras

Grant Cairns·Nguyen Thanh Tung Le·Anthony Nielsen·Yuri Nikolayevsky
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Abstract

We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand, we give an example of a solvable unimodular Lie algebra of dimension 5 that has no orthonormal geodesic basis, for any inner product.

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Grant Cairns, Nguyen Thanh Tung Le, Anthony Nielsen, Yuri Nikolayevsky. 2013-02-12. On the existence of orthonormal geodesic bases for Lie algebras. https://arxiv.org/abs/1302.2751

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