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}
}