Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02130 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910719314755584 |
|---|---|
| author | Torres-Gomez, Alexander Valencia, Fabricio |
| author_facet | Torres-Gomez, Alexander Valencia, Fabricio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Double extension of flat pseudo-Riemannian $F$-Lie algebras Torres-Gomez, Alexander Valencia, Fabricio Differential Geometry Rings and Algebras 53D45, 16E40, 17A30, 22F30, 17B63 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. |
| title | Double extension of flat pseudo-Riemannian $F$-Lie algebras |
| topic | Differential Geometry Rings and Algebras 53D45, 16E40, 17A30, 22F30, 17B63 |
| url | https://arxiv.org/abs/2405.02130 |