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Ergodic Theory and Semisimple Groups

  • Book
  • © 1984

Overview

Authors:
  1. Robert J. Zimmer
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Part of the book series: Monographs in Mathematics (MMA, volume 81)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Robert J. Zimmer
    Pages 1-7

  3. Moore’s Ergodicity Theorem

    • Robert J. Zimmer
    Pages 8-31

  4. Algebraic Groups and Measure Theory

    • Robert J. Zimmer
    Pages 32-58

  5. Amenability

    • Robert J. Zimmer
    Pages 59-84

  6. Rigidity

    • Robert J. Zimmer
    Pages 85-113

  7. Margulis’ Arithmeticity Theorems

    • Robert J. Zimmer
    Pages 114-129

  8. Kazhdan’s Property (T)

    • Robert J. Zimmer
    Pages 130-148

  9. Normal Subgroups of Lattices

    • Robert J. Zimmer
    Pages 149-161

  10. Further Results on Ergodic Actions

    • Robert J. Zimmer
    Pages 162-186

  11. Generalizations to p-adic groups and S-arithmetic groups

    • Robert J. Zimmer
    Pages 187-193

  12. Back Matter

    Pages 194-209
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Keywords

About this book

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 anumber 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.

Bibliographic Information

  • Book Title: Ergodic Theory and Semisimple Groups

  • Authors: Robert J. Zimmer

  • Series Title: Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9488-4

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1984

  • Softcover ISBN: 978-1-4684-9490-7Published: 11 January 2013

  • eBook ISBN: 978-1-4684-9488-4Published: 14 March 2013

  • Series ISSN: 1017-0480

  • Series E-ISSN: 2296-4886

  • Edition Number: 1

  • Number of Pages: X, 209

  • Topics: Dynamical Systems and Ergodic Theory, Group Theory and Generalizations

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