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Lattices acting on right-angled buildings. (English) Zbl 1128.22002

Summary: Let \(X\) be a right-angled building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut\((X)\), and show that the group Aut\((X)\) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of groups to complexes of groups.

MSC:

22D05 General properties and structure of locally compact groups
20E42 Groups with a \(BN\)-pair; buildings
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