Density of commensurators for uniform lattices of right-angled buildings

Kubena, A. and Thomas, A. (2012) Density of commensurators for uniform lattices of right-angled buildings. Journal of Group Theory, 15(5), pp. 565-611. (doi: 10.1515/jgt-2012-0017)

Abstract

Let G be the automorphism group of a regular right-angled building X. The “standard uniform lattice” is a canonical graph product of finite groups, which acts discretely on X with quotient a chamber. We prove that the commensurator of is dense in G. This result was also obtained by Haglund (2008). For our proof, we develop carefully a technique of “unfoldings” of complexes of groups. We use unfoldings to construct a sequence of uniform lattices , each commensurable to , and then apply the theory of group actions on complexes of groups to the sequence . As further applications of unfoldings, we determine exactly when the group G is nondiscrete, and prove that G acts strongly transitively on X.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Thomas, Dr Anne
• Authors: Kubena, A., and Thomas, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Group Theory
• ISSN: 1433-5883
• ISSN (Online): 1435-4446