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Born Lie algebras

Differential Geometry 2025-05-13 v2 Mathematical Physics math.MP

Abstract

We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie algebras up to dimension four and all six-dimensional nilpotent Lie algebras admitting an integrable Born structure. Finally, we study the curvature properties of the pseudo-Riemannian metrics of the integrable Born structures obtained in our classification results.

Keywords

Cite

@article{arxiv.2411.04856,
  title  = {Born Lie algebras},
  author = {Alejandro Gil-García and Paula Naomi Pilatus},
  journal= {arXiv preprint arXiv:2411.04856},
  year   = {2025}
}

Comments

23 pages. Journal version

R2 v1 2026-06-28T19:51:48.162Z