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.