An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
The Reflective Lorentzian Lattices of Rank 3

Daniel Allcock University of Texas at Austin, Austin, TX
Available Formats:
Electronic ISBN: 978-0-8218-9203-9
Product Code: MEMO/220/1033.E
108 pp
List Price: $70.00 MAA Member Price:$63.00
AMS Member Price: $42.00 Click above image for expanded view The Reflective Lorentzian Lattices of Rank 3 Daniel Allcock University of Texas at Austin, Austin, TX Available Formats:  Electronic ISBN: 978-0-8218-9203-9 Product Code: MEMO/220/1033.E 108 pp  List Price:$70.00 MAA Member Price: $63.00 AMS Member Price:$42.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2202012
MSC: 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.

• Chapters
• Introduction
• 1. Background
• 2. The Classification Theorem
• 3. The Reflective Lattices
• Request Review Copy
• Get Permissions
Volume: 2202012
MSC: 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.

• Chapters
• Introduction
• 1. Background
• 2. The Classification Theorem
• 3. The Reflective Lattices
Please select which format for which you are requesting permissions.