University Lecture Series
Volume: 66;
2016;
160 pp;
Softcover
MSC: Primary 20;
Secondary 14
Print ISBN: 978-1-4704-3105-1
Product Code: ULECT/66
List Price: $35.00
AMS Member Price: $28.00
MAA Member Price: $31.50
Electronic ISBN: 978-1-4704-3631-5
Product Code: ULECT/66.E
List Price: $35.00
AMS Member Price: $28.00
MAA Member Price: $31.50
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Supplemental Materials
Lectures on Chevalley Groups
Share this pageRobert Steinberg
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
Readership
Undergraduate and graduate students and researchers interested in algebraic groups.
Reviews & Endorsements
This is the first formal publication of the well-known set of notes from lectures given by R. Steinberg at Yale University in 1967 and initially issued in mimeographed form. Despite their limited circulation, these notes have served as the standard reference for an introduction to the theory of Chevalley groups. Before this publication, to get your hands on this masterly exposition, you had to hope that your local library had a copy or a copy of a copy of it. I must emphasize that, as anyone involved in these subjects knows, that the exposition in these lectures includes many original contributions of the author that have now become the standard ones which one finds in the literature. The AMS edition of these notes has been reset in LaTeX and includes some corrections and a few additions by Steinberg himself.
-- Felipe Zaldivar, MAA Reviews
This book is most welcome.
-- Wilberd van der Kallen, Zentralblatt MATH
Table of Contents
Table of Contents
Lectures on Chevalley Groups
- Cover Cover11
- Title page iii4
- Contents v6
- Foreword vii8
- Acknowledgement ix10
- Preface xi12
- Chapter 0. Introduction 114
- Chapter 1. A basis for \calL 518
- Chapter 2. A basis for \calU 1124
- Chapter 3. The Chevalley Groups 1932
- Chapter 4. Simplicity of ๐บ 3346
- Chapter 5. Chevalley Groups and Algebraic Groups 3750
- Chapter 6. Generators and Relations 4356
- Chapter 7. Central Extensions 4760
- Chapter 8. Variants of the Bruhat Lemma 6174
- Chapter 9. The Orders of the Finite Chevalley Groups 7790
- Chapter 10. Isomorphisms and Automorphisms 8598
- Chapter 11. Some Twisted Groups 99112
- Chapter 12. Representations 117130
- Chapter 13. Representations Continued 129142
- Chapter 14. Representations Completed 137150
- Appendix on Finite Reflection Groups 149162
- Bibliography 155168
- Index 159172
- Back Cover Back Cover1175