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Self-similar periodic tilings on the Heisenberg group. (English) Zbl 0829.22018

Let \(G\) be the Heisenberg Lie group. The author constructs a tiling on \(G\), so that the discrete cocompact subgroup consisting of all elements of \(G\) with integral coordinates, acting on \(G\) by left multiplication, acts freely and transitively on the set of tiles.

MSC:

22E40 Discrete subgroups of Lie groups
53C20 Global Riemannian geometry, including pinching
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