The reflective Lorentzian lattices of rank 3
Daniel 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
Kategori:
Tahun:
2012
Penerbit:
Amer Mathematical Society
Bahasa:
english
Halaman:
125
ISBN 10:
0821869116
ISBN 13:
9780821869116
Nama siri:
Memoirs of the American Mathematical Society 1033
Fail:
PDF, 910 KB
IPFS:
,
english, 2012