# Discrete Linear Groups containing Arithmetic Groups

Abstract : We prove in a large number of cases, that a Zariski dense discrete subgroup of a simple real algebraic group $G$ which contains a higher rank lattice is a lattice in the group $G$. For example, we show that a Zariski dense subgroup of $SL_n({\mathbb R})$ which contains $SL_3({\mathbb Z})$ in the top left hand corner, is conjugate to $SL_n({\mathbb Z})$ .
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00470793
Contributor : Indira Chatterji <>
Submitted on : Wednesday, April 7, 2010 - 1:24:16 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM

### Identifiers

• HAL Id : hal-00470793, version 1
• ARXIV : 0905.1813

### Citation

Indira Chatterji, T. N. Venkataramana. Discrete Linear Groups containing Arithmetic Groups. 2009. ⟨hal-00470793⟩

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