Automorphism groups of right-angled buildings: simplicity and local splittings

Abstract

We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly) simple locally compact groups. Specializing to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products.

26 pages. Several points were clarified and a few lemmas were added, in accordance with the referee's report

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