The Reflective Lorentzian Lattices of Rank 3
The Reflective Lorentzian Lattices of Rank 3
复制标题
3阶反射洛伦兹晶格
DOI：
10.1090/s0065-9266-2012-00648-4
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Daniel Allcock
中科院分区：
文献类型：
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作者：
Daniel Allcock
对签名$(2，1)$的所有对称整数双线性形式进行了分类，其等距群是通过反射生成的，直到有限指数。达到规模的有8,595个，它们的374个不同的Weyl基团分为39个可公度类。这推广了Niklin对强无平方情形的列举。作者的技术是对Weyl腔的形状进行分析，然后使用Vinberg的算法和“双射方法”进行计算机工作。他还纠正了康威和斯隆对其规范的$2$-ady符号的定义中的一个小错误。
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.