درس‌گفتارهایی دربارهٔ گروه‌های شوالیه (سری سخنرانی‌های دانشگاهی)

Robert Steinberg's Lectures on Chevalley Groups were delivered and written during the author's sabbatical visit to Yale University in the 1967-1968 academic year. The work presents the status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in the subsequent classification of finite groups. This posthumous edition incorporates additions and corrections prepared by the author during his retirement, including a new introductory chapter. A bibliography and editorial notes have also been added. This is a great unsurpassed introduction to the subject of Chevalley groups that influenced generations of mathematicians. I would recommend it to anybody whose interests include group theory. -Efim Zelmanov, University of California, San Diego Robert Steinberg's lectures on Chevalley groups were given at Yale University in 1967. The notes for the lectures contain a wonderful exposition of the work of Chevalley, as well as important additions to that work due to Steinberg himself. The theory of Chevalley groups is of central importance not only for group theory, but also for number theory and theoretical physics, and is as relevant today as it was in 1967. The publication of these lecture notes in book form is a very welcome addition to the literature. -George Lusztig, Massachusetts Institute of Technology Robert Steinberg gave a course at Yale University in 1967 and the mimeographed notes of that course have been read by essentially anyone interested in Chevalley groups. In this course, Steinberg presents the basic constructions of the Chevalley groups over arbitrary fields. He also presents fundamental material about generators and relations for these groups and automorphism groups. Twisted variations on the Chevalley groups are also introduced. There are several chapters on the representation theory of the Chevalley groups (over an arbitrary field) and for many of the finite twisted groups. Even 50 years later, this book is still one of the best introductions to the theory of Chevalley groups and should be read by anyone interested in the field. -Robert Guralnick, University of Southern California A Russian translation of this lecture course by Robert Steinberg was published in Russia more than 40 years ago, but for some mysterious reason has never been published in the original language. This book is very dear to me. It is not only an important advance in the theory of algebraic groups, but it has also played a key role in more recent developments of the theory of Kac-Moody groups. The very different approaches, one by Tits and another by Peterson and myself, borrowed heavily from this remarkable book. -Victor Kac, Massachusetts Institute of Technology - See more at: http://bookstore.ams.org/ulect-66#sthash.Nt1NxZZI.dpuf Cover -- Title page -- Contents -- Foreword -- Acknowledgement -- Preface -- Chapter 0. Introduction -- Chapter 1. A basis for \calL -- Chapter 2. A basis for \calU -- Chapter 3. The Chevalley Groups -- Chapter 4. Simplicity of -- Chapter 5. Chevalley Groups and Algebraic Groups -- Chapter 6. Generators and Relations -- Chapter 7. Central Extensions -- Chapter 8. Variants of the Bruhat Lemma -- Chapter 9. The Orders of the Finite Chevalley Groups -- Chapter 10. Isomorphisms and Automorphisms -- Chapter 11. Some Twisted Groups -- Chapter 12. Representations -- Chapter 13. Representations Continued -- Chapter 14. Representations Completed -- Appendix on Finite Reflection Groups -- I. Preliminaries -- II. The Function -- III. A Fundamental Domain for -- IV. Generators and relations for -- V. Appendix -- Bibliography -- Index -- Back Cover Cover Title page Contents Foreword Acknowledgement Preface Chapter 0. Introduction Chapter 1. A basis for \calL Chapter 2. A basis for \calU Chapter 3. The Chevalley Groups Chapter 4. Simplicity of G Chapter 5. Chevalley Groups and Algebraic Groups Chapter 6. Generators and Relations Chapter 7. Central Extensions Chapter 8. Variants of the Bruhat Lemma Chapter 9. The Orders of the Finite Chevalley Groups Chapter 10. Isomorphisms and Automorphisms Chapter 11. Some Twisted Groups Chapter 12. Representations Chapter 13. Representations Continued Chapter 14. Representations Completed Appendix on Finite Reflection Groups I. Preliminaries II. The Function N III. A Fundamental Domain for W IV. Generators and relations for W V. Appendix Bibliography Index Back Cover