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arXiv · 2405.02130

Double extension of flat pseudo-Riemannian $F$-Lie algebras

Alexander Torres-Gomez·Fabricio Valencia
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Abstract

We define the concept of a flat pseudo-Riemannian $F$-Lie algebra and construct its corresponding double extension. This algebraic structure can be interpreted as the infinitesimal analogue of a Frobenius Lie group devoid of Euler vector fields. We show that the double extension provides a framework for generating all weakly flat Lorentzian non-abelian bi-nilpotent $F$-Lie algebras possessing one dimensional light-cone subspaces. A similar result can be established for nilpotent Lie algebras equipped with flat scalar products of signature $(2,n-2)$ where $n\geq 4$. Furthermore, we use this technique to construct Poisson algebras exhibiting compatibility with flat scalar products.

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Alexander Torres-Gomez, Fabricio Valencia. 2024-05-03. Double extension of flat pseudo-Riemannian $F$-Lie algebras. https://arxiv.org/abs/2405.02130

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