# Super-Rigidity and non-linearity for lattices in products

## TL;DR

This paper establishes super-rigidity results for certain lattices in product groups and provides criteria to determine when these groups are non-linear, advancing understanding of their algebraic and representation-theoretic properties.

## Contribution

It introduces new super-rigidity theorems for lattices in product groups and offers criteria for their non-linearity, extending previous rigidity and non-linearity results.

## Key findings

- Proves super-rigidity for irreducible lattices in product groups.
- Derives criteria for non-linearity of these lattices.
- Enhances understanding of algebraic representations over complete fields.

## Abstract

We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in product of groups and lattices with dense commensurator groups. We derive some criteria for non-linearity of such groups.