Solvable lattices and their groups of automorphisms

G. A. Soifer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The main goal of this paper is to construct an "algebraic" representation of a group automorphisms Aut Γ for any elementary solvable group Γ. "Algebraic" means that the image of a semisimple (unipotent) automorphism, in the sense of Wang, will be a semisimple (unipotent) matrix Theorem 1. This gives an answer on the question asking by Wang. As a corollary of this theorem, we show that for any group of automorphisms Aut Γ of a lattice Γ in a solvable connected group Lie G there exist a representation ρ : Aut Γ → GLn(ℤ), such that ρ(Aut Γ) is an arithmetic subgroup in the Zariski closure ρ(Aut Γ).

Original languageEnglish
Pages (from-to)805-817
Number of pages13
JournalCommunications in Algebra
Issue number3
StatePublished - 2004

Bibliographical note

Funding Information:
It is also a pleasure for me to thank the Isaac Newton Mathematical Institute, University of Cambridge and SFB343, Bielefeld University for their support and hospitality, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University, and the Center of Excellence, supported by ISF, grant N 8008/02-1.


  • Arithmetic subgroup
  • Automorphism
  • Lattice


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