Introduction to arithmetic groups. Translated from the French by Lam Laurent Pham. Translation edited and with a preface by Dave Witte Morris. (English) Zbl 1432.22016
University Lecture Series 73. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5231-5/pbk; 978-1-4704-5431-9/ebook). xii, 118 p. (2019).
This classic by A. Borel is, despite its age, still a standard reference for arithmetic groups and reduction theory. The French original has been extensively discussed in [Introduction aux groupes arithmétiques. Paris: Hermann & Cie (1969; Zbl 0186.33202)]. The current reviewer finds little to add to these well founded reviews.
This English translation is a valuable addendum by two reasons.
Firstly, because it is in English and thus makes the text available to a wider audience and secondly because of the 182 footnotes which have been added and are due to Dave (Witte) Morris. These footnotes make the demanding text much more accessible and are as such already a precious addition to the literature. Having them come with the English translation is a wonderful idea and will boost the readership of this significant text.
This English translation is a valuable addendum by two reasons.
Firstly, because it is in English and thus makes the text available to a wider audience and secondly because of the 182 footnotes which have been added and are due to Dave (Witte) Morris. These footnotes make the demanding text much more accessible and are as such already a precious addition to the literature. Having them come with the English translation is a wonderful idea and will boost the readership of this significant text.
Reviewer: Anton Deitmar (Tübingen)
MSC:
| 22E40 | Discrete subgroups of Lie groups |
| 22-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups |
| 01A75 | Collected or selected works; reprintings or translations of classics |
| 11F06 | Structure of modular groups and generalizations; arithmetic groups |
| 14Lxx | Algebraic groups |
| 20G20 | Linear algebraic groups over the reals, the complexes, the quaternions |
| 20G30 | Linear algebraic groups over global fields and their integers |
