Volume: 73; 2019; 118 pp; Softcover
MSC: Primary 22; Secondary 11; 20
Print ISBN: 978-1-4704-5231-5
Product Code: ULECT/73
List Price: $50.00
AMS Member Price: $40.00
MAA Member Price: $45.00
Electronic ISBN: 978-1-4704-5431-9
Product Code: ULECT/73.E
List Price: $50.00
AMS Member Price: $40.00
MAA Member Price: $45.00
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Supplemental Materials
Introduction to Arithmetic Groups
Share this pageArmand Borel
Fifty years after it made the transition from
mimeographed lecture notes to a published book, Armand Borel's
Introduction aux groupes arithmétiques continues to be
very important for the theory of arithmetic groups. In particular,
Chapter III of the book remains the standard reference for fundamental
results on reduction theory, which is crucial in the study of discrete
subgroups of Lie groups and the corresponding homogeneous spaces.
The review of the original French version in Mathematical
Reviews observes that “the style is concise and the proofs (in later
sections) are often demanding of the reader.” To make the
translation more approachable, numerous footnotes provide helpful
comments.
Readership
Graduate students and researchers interested in the theory of algebraic groups.
Reviews & Endorsements
Borel's 'Introduction aux groupes arithmétiques' is a classic that has served generations of graduate students and researchers interested in arithmetic subgroups of algebraic groups. The AMS has done a huge service to this community by making an English translation of the book available.
-- Benjamin Linowitz, MAA Reviews
Table of Contents
Table of Contents
Introduction to Arithmetic Groups
- Cover 11
- Title page 44
- Preface to the English Translation 88
- Introduction 1010
- Notation 1212
- Chapter I. Some Classical Groups 1414
- Chapter II. Algebraic Groups 4444
- Chapter III. Fundamental Sets with Cusps 6868
- 10. Algebraic tori 6868
- 11. Parabolic subgroups. Bruhat decomposition 7373
- 12. Siegel sets 8787
- 13. Fundamental sets (second type) 9292
- 14. Fundamental representations. Associated functions 9797
- 15. The Siegel property 101101
- 16. Fundamental sets and minima 111111
- 17. Groups with rational rank one 121121
- Bibliography 128128
- Index 130130
- Back Cover 133133