English

Approximate Lattices and Meyer Sets in Nilpotent Lie Groups

Group Theory 2020-04-02 v3

Abstract

We show that uniform approximate lattices in nilpotent Lie groups are subsets of model sets. This extends a theorem due to Yves Meyer about quasicrystals in Euclidean spaces. To do so we study relatively dense subsets of simply connected nilpotent Lie groups and their logarithms. We then deduce a simple criterion for the existence of an approximate lattice in a given nilpotent Lie group.

Keywords

Cite

@article{arxiv.1810.10870,
  title  = {Approximate Lattices and Meyer Sets in Nilpotent Lie Groups},
  author = {Simon Machado},
  journal= {arXiv preprint arXiv:1810.10870},
  year   = {2020}
}
R2 v1 2026-06-23T04:52:32.196Z