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The Reflective Lorentzian Lattices of Rank 3
 
Daniel Allcock University of Texas at Austin, Austin, TX
The Reflective Lorentzian Lattices of Rank 3
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
The Reflective Lorentzian Lattices of Rank 3
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The Reflective Lorentzian Lattices of Rank 3
Daniel Allcock University of Texas at Austin, Austin, TX
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2202012; 108 pp
    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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Background
    • 2. The Classification Theorem
    • 3. The Reflective Lattices
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2202012; 108 pp
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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.