Unfaithful complex hyperbolic triangle groups, I: Involutions
Unfaithful complex hyperbolic triangle groups, I: Involutions
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DOI：
10.2140/pjm.2008.238.145
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发表时间：
2008-11
影响因子：
0.6
通讯作者：
J. Parker
中科院分区：
文献类型：
--
作者：
J. Parker
复双曲三角形群是复双曲空间中由固定三条复直线的复对合生成的复双曲等距群。这样一个群称为等边群，如果存在一个三阶等距线循环置换这三条复直线。我们考虑等边三角形群，其中每对对合的乘积和所有三个对合的乘积都是非斜驶的。我们对所有这些离散的群进行分类。
A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the product of all three involutions are all nonloxodromic. We classify all such groups that are discrete.