We prove that an irreducible lattice in a semisimple algebraic group is virtually isomorphic to an arithmetic lattice if and only if it admits a faithful self-similar action on a rooted tree of finite valency.
Cite this article
Michael Kapovich, Arithmetic aspects of self-similar groups. Groups Geom. Dyn. 6 (2012), no. 4, pp. 737–754DOI 10.4171/GGD/172