The Reflective Lorentzian Lattices of Rank 3 - Memoirs of the American Mathematical Society (Paperback)Daniel Allcock (author)
Paperback 108 Pages / Published: 30/12/2012
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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.
Publisher: American Mathematical Society
Number of pages: 108
Dimensions: 254 x 178 mm
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