On the existence of orthonormal geodesic bases for Lie algebras

Authors

  • Grant Cairns
  • Nguyen Thanh Tung Le
  • Anthony Nielsen
  • Yuri Nikolayevsky

DOI:

https://doi.org/10.1285/i15900932v33n2p11

Keywords:

geodesic vector, unimodular Lie algebra

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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Published

12-02-2014

Issue

Volume 33, Issue 2 (2013)

Section

Articoli

License

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Gli autori che pubblicano in questa rivista accettano i termini e le condizioni specificate nella licenza Creative Commons di cui al link sottostante.

http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode