Splittable Lattices in the metabelian solvable Lie group $\mathbb{R}^n\rtimes\mathbb{R}^m$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917113905545216 |
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| author | Dali, Béchir Riahi, Moncef |
| author_facet | Dali, Béchir Riahi, Moncef |
| contents | The purpose of this note is describe and classify the splittable lattices in the completely solvable metabelian Lie group (semidirect product of abelian vector groups) $G:=\mathbb{R}^n\rtimes_η\mathbb{R}^m$, where $η$ is the continuous representation of the topological additive abelian group $\mathbb R^m$ in $\mathbb R^n$ given by $η(t_1,\dots, t_m)=\exp(\sum_{j=1}^{m}t_jΔ_j)$ with $(Δ_j)_{1\leq j\leq m}$ is a set of pairwise commuting diagonal matrices in $\mathbb R^{n\times n}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_00472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Splittable Lattices in the metabelian solvable Lie group $\mathbb{R}^n\rtimes\mathbb{R}^m$ Dali, Béchir Riahi, Moncef Differential Geometry 22E25, 22E40 The purpose of this note is describe and classify the splittable lattices in the completely solvable metabelian Lie group (semidirect product of abelian vector groups) $G:=\mathbb{R}^n\rtimes_η\mathbb{R}^m$, where $η$ is the continuous representation of the topological additive abelian group $\mathbb R^m$ in $\mathbb R^n$ given by $η(t_1,\dots, t_m)=\exp(\sum_{j=1}^{m}t_jΔ_j)$ with $(Δ_j)_{1\leq j\leq m}$ is a set of pairwise commuting diagonal matrices in $\mathbb R^{n\times n}$. |
| title | Splittable Lattices in the metabelian solvable Lie group $\mathbb{R}^n\rtimes\mathbb{R}^m$ |
| topic | Differential Geometry 22E25, 22E40 |
| url | https://arxiv.org/abs/2512.00472 |