## Abstract

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 → GL_{n}(ℤ), such that ρ(Aut Γ) is an arithmetic subgroup in the Zariski closure ρ(Aut Γ).

Original language | English |
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Pages (from-to) | 805-817 |

Number of pages | 13 |

Journal | Communications in Algebra |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - 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.

### Funding

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.

Funders | Funder number |
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Emmy Noether Research Institute for Mathematics, Bar-Ilan University | |

University of Cambridge | SFB343 |

Israel Science Foundation | N 8008/02-1 |

Universität Bielefeld |

## Keywords

- Arithmetic subgroup
- Automorphism
- Lattice