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Softcover ISBN:  9781470431051 
Product Code:  ULECT/66 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470436315 
Product Code:  ULECT/66.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9781470431051 
eBook ISBN:  9781470436315 
Product Code:  ULECT/66.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 66; 2016; 160 ppMSC: Primary 20; Secondary 14
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 mid1960s. 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 KacMoody 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
ReadershipUndergraduate and graduate students and researchers interested in algebraic groups.

Table of Contents

Chapters

Chapter 0. Introduction

Chapter 1. A basis for $\mathcal {L}$

Chapter 2. A basis for $\mathcal {U}$

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


Additional Material

Reviews

This is the first formal publication of the wellknown 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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
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 Reviews
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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 mid1960s. 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 KacMoody 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
Undergraduate and graduate students and researchers interested in algebraic groups.

Chapters

Chapter 0. Introduction

Chapter 1. A basis for $\mathcal {L}$

Chapter 2. A basis for $\mathcal {U}$

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

This is the first formal publication of the wellknown 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