| eBook ISBN: | 978-0-8218-9203-9 |
| Product Code: | MEMO/220/1033.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
| eBook ISBN: | 978-0-8218-9203-9 |
| Product Code: | MEMO/220/1033.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 220; 2012; 108 ppMSC: Primary 11; Secondary 20; 22
The author classifies all the symmetric integer bilinear forms of signature \((2,1)\) whose isometry groups are generated up to finite index by reflections. There are 8,595 of them up to scale, whose 374 distinct Weyl groups fall into 39 commensurability classes. This extends Nikulin's enumeration of the strongly square-free cases. The author's technique is an analysis of the shape of the Weyl chamber, followed by computer work using Vinberg's algorithm and a “method of bijections”. He also corrects a minor error in Conway and Sloane's definition of their canonical \(2\)-adic symbol.
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Table of Contents
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Chapters
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Introduction
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1. Background
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2. The Classification Theorem
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3. The Reflective Lattices
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The author classifies all the symmetric integer bilinear forms of signature \((2,1)\) whose isometry groups are generated up to finite index by reflections. There are 8,595 of them up to scale, whose 374 distinct Weyl groups fall into 39 commensurability classes. This extends Nikulin's enumeration of the strongly square-free cases. The author's technique is an analysis of the shape of the Weyl chamber, followed by computer work using Vinberg's algorithm and a “method of bijections”. He also corrects a minor error in Conway and Sloane's definition of their canonical \(2\)-adic symbol.
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Chapters
-
Introduction
-
1. Background
-
2. The Classification Theorem
-
3. The Reflective Lattices
