Memoirs of the American Mathematical Society
2012;
108 pp;
Softcover
MSC: Primary 11;
Secondary 20; 22
Print ISBN: 978-0-8218-6911-6
Product Code: MEMO/220/1033
List Price: $70.00
AMS Member Price: $42.00
MAA Member Price: $63.00
Electronic ISBN: 978-0-8218-9203-9
Product Code: MEMO/220/1033.E
List Price: $70.00
AMS Member Price: $42.00
MAA Member Price: $63.00
The Reflective Lorentzian Lattices of Rank 3
Share this pageDaniel Allcock
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.