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Ergodic Theory and Semisimple Groups

  • Authors
  • Robert J. Zimmer

Part of the Monographs in Mathematics book series (MMA, volume 81)

Table of contents

  1. Front Matter
    Pages i-x
  2. Robert J. Zimmer
    Pages 1-7
  3. Robert J. Zimmer
    Pages 8-31
  4. Robert J. Zimmer
    Pages 32-58
  5. Robert J. Zimmer
    Pages 59-84
  6. Robert J. Zimmer
    Pages 85-113
  7. Robert J. Zimmer
    Pages 114-129
  8. Robert J. Zimmer
    Pages 130-148
  9. Robert J. Zimmer
    Pages 149-161
  10. Robert J. Zimmer
    Pages 162-186
  11. Back Matter
    Pages 194-209

About this book

Introduction

This book is based on a course given at the University of Chicago in 1980-81. As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background, of the profound work of G. A. Margulis concerning rigidity, arithmeticity, and structure of lattices in semi­ simple groups, and related work of the author on the actions of semisimple groups and their lattice subgroups. In doing so, we develop the necessary prerequisites from earlier work of Borel, Furstenberg, Kazhdan, Moore, and others. One of the difficulties involved in an exposition of this material is the continuous interplay between ideas from the theory of algebraic groups on the one hand and ergodic theory on the other. This, of course, is not so much a mathematical difficulty as a cultural one, as the number of persons comfortable in both areas has not traditionally been large. We hope this work will also serve as a contribution towards improving that situation. While there are a number of satisfactory introductory expositions of the ergodic theory of integer or real line actions, there is no such exposition of the type of ergodic theoretic results with which we shall be dealing (concerning actions of more general groups), and hence we have assumed absolutely no knowledge of ergodic theory (not even the definition of "ergodic") on the part of the reader. All results are developed in full detail.

Keywords

Arithmetic Identity Lattice algebra ergodic theory theorem

Bibliographic information