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.
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