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- Title
Abstract commensurators of lattices in Lie groups.
- Authors
Studenmund, Daniel
- Abstract
Let Γ be a lattice in a simply-connected solvable Lie group. We construct a ℚ- defined algebraic group A such that the abstract commensurator of Γ is isomorphic to A(ℚ) and Aut(Γ) is commensurable with A(ℤ). Our proof uses the algebraic hull construction, due to Mostow, to define an algebraic group H so that commensurations of Γ extend to ℚ-defined automorphisms of H. We prove an analogous result for lattices in connected linear Lie groups whose semisimple quotient satisfies superrigidity.
- Subjects
ABSTRACT algebra; COMMENSURATE-incommensurate transitions; LIE groups; DIFFERENTIAL algebraic groups; SUBMANIFOLDS
- Publication
Commentarii Mathematici Helvetici, 2015, Vol 90, Issue 2, p287
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/354