Is the right-angled building associated to a universal group unique?

Abstract

A universal group is a subgroup of the group of type-preserving automorphisms of a right-angled building and hence associated to this building. A question is then whether this universal group can act chamber-transitively and with compact open stabilisers on a different right-angled building of the same type. We answer this question and define two universal groups associated to different right-angled buildings which are isomorphic as topological groups. Moreover, we show that different right-angled buildings can have the same universal group.