Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Matrix entries, unipotents, and linearity of amalgams

Sami Douba, Konstantinos Tsouvalas

Abstract

We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated residually finite groups that fail to be linear.

Matrix entries, unipotents, and linearity of amalgams

Abstract

We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated residually finite groups that fail to be linear.
Paper Structure (5 sections, 23 theorems, 27 equations)

This paper contains 5 sections, 23 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Doubling along subgroups detected by the top-left entry
  3. Doubling along intersections with compact subgroups
  4. Doubling along cocompact stabilizers
  5. Doubling along noncocompact lattices

Key Result

Theorem 1.1

Let $\mathsf{G}$ be a semisimple real algebraic group with no compact factors that is not locally isomorphic to $\mathsf{O}(n,1)$ or $\mathsf{U}(n,1)$ for any $n\in \mathbb{N}$, and let $\Gamma < \mathsf{G}$ be an irreducible lattice. If $\Lambda$ is an infinite-index subgroup of $\Gamma$ that is no

Theorems & Definitions (51)

  • Theorem 1.1
  • Theorem 1.2
  • Corollary 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Theorem 1.6
  • Theorem 1.7
  • Theorem 2.1
  • proof : Proof of Theorem \ref{['main']}(\ref{['main-item1']})
  • proof : Proof of Theorem \ref{['main']} (\ref{['main-item2']})
  • ...and 41 more