Approximate Lattices and Meyer Sets in Nilpotent Lie Groups

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.

References in corpus (1)

• Automorphisms of real Lie algebras of dimension five or less

Cited by in corpus (3)

• Borel density for approximate lattices
• Closed approximate subgroups: compactness, amenability and approximate lattices
• Linear repetitivity beyond abelian groups