Born Lie algebras
Alejandro Gil-Garc\'ia, Paula Naomi Pilatus

TL;DR
This paper classifies low-dimensional Lie algebras with Born structures, showing they can be constructed via bicross products from pseudo-Riemannian Lie algebras, and analyzes their curvature properties.
Contribution
It introduces a classification of low-dimensional Born Lie algebras and explores their geometric and curvature characteristics.
Findings
All 4-dimensional Lie algebras with Born structures are classified.
Six-dimensional nilpotent Lie algebras with integrable Born structures are characterized.
Curvature properties of the associated pseudo-Riemannian metrics are analyzed.
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.
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Taxonomy
TopicsAdvanced Topics in Algebra
