Abstract commensurators of lattices in Lie groups

  • Daniel Studenmund

    University of Chicago, USA

Abstract

Let be a lattice in a simply-connected solvable Lie group. We construct a -defined algebraic group such that the abstract commensurator of is isomorphic to and Aut is commensurable with . Our proof uses the algebraic hull construction, due to Mostow, to define an algebraic group so that commensurations of extend to -defined automorphisms of . We prove an analogous result for lattices in connected linear Lie groups whose semisimple quotient satisfies superrigidity.

Cite this article

Daniel Studenmund, Abstract commensurators of lattices in Lie groups. Comment. Math. Helv. 90 (2015), no. 2, pp. 287–323

DOI 10.4171/CMH/354