Proc. Inst. Wrk.shps. Int. Conf. – Essays in Geometric Group Theory No. 9, 2009, pp. 79–104. Commensurators of Some Non-uniform Tree Lattices and Moufang Twin Trees Peter Abramenko1 and Bertrand Remy2 1Department of Mathematics, Institut Camille Jordan – UMR CNRS, University of Virginia, Universite Claude Bernard – Lyon 1, P.O. Box 400137, Charlottesville 221 rue Claude Bernard, VA 22904 4137 – USA, 69622 Villeurbanne cedex, France e-mail: ; Abstract. Sh. Mozes showed that the commensurator of the lattice PSL2(Fp[t?1]) is dense in the full automorphism group of the Bruhat–Tits tree of valency p + 1, the latter group being much bigger than PSL2(Fp((t))). By G.A. Margulis's criterion, this density is a generalized arithmeticity result. We show that the density of the commensurator holds for many tree-lattices among those called of Nagao type by H. Bass and A. Lubotzky. The result covers many lattices obtained via Moufang twin trees. Keywords. Tree, lattice of Nagao type, commensurator, twinning, Moufang property Kac-Moody group. Subject Classification: 22F50, 22E20, 51E24, 22E40 Introduction Tree lattices have been and still are the subject of a lot of interesting mathematical research, see in particular the monograph [BL01] and the papers cited there.
- group
- finite covolume
- nagao lattice
- tree-lattices among
- lattice described
- moufang twin
- lattices obtained via moufang twin
- finite