On the existence of orthonormal geodesic bases for Lie algebras


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.

DOI Code: 10.1285/i15900932v33n2p11

Keywords: geodesic vector; unimodular Lie algebra

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