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ALLIANCE DIAMOND OPEN ACCESS JOURNALS
DOI: 10.19086/da.11886
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We show that uniform approximate lattices in nilpotent Lie groups are subsets of model sets. This extends Yves Meyer's theorem about quasi-crystals 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.
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