Journal
MATHEMATISCHE ANNALEN
Volume 382, Issue 1-2, Pages 285-301Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00208-021-02258-8
Keywords
Approximate lattices; Approximate subgroups; Lie groups; Linear algebraic groups
Categories
Funding
- UK Engineering and Physical Sciences Research Council (EPSRC) [EP/L016516/1]
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The study investigates infinite approximate subgroups of soluble Lie groups, showing their proximity to genuine connected subgroups in a defined sense. Building on this, a structure theorem for approximate lattices in soluble Lie groups is proved, extending Yves Meyer's theorem on quasi-crystals to the context of soluble Lie groups.
We study infinite approximate subgroups of soluble Lie groups. We show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building upon this result we prove a structure theorem for approximate lattices in soluble Lie groups. This extends to soluble Lie groups a theorem about quasi-crystals due to Yves Meyer.
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