论文标题
关于较高级别谎言组的晶格的刚性刚度
On the profinite rigidity of lattices in higher rank Lie groups
论文作者
论文摘要
我们研究哪些较高的简单谎言组有限地接受但不抽象地归功于晶格。我们表明，类型$ e_8 $，$ f_4 $和$ g_2 $的复杂形式的复杂形式不存在此类示例。相比之下，除其他所有较高等级的谎言组中，都有许多此类示例，除了可能$ \ mathrm {sl} _ {2n+1}（\ Mathbb {r}）$，$ \ mathrm {sl} _ {2n+1}（ $ \ mathrm {sl} _n（\ mathbb {h}）$或类型$ e_6 $的组。
We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E_8$, $F_4$, and $G_2$. In contrast, there are arbitrarily many such examples in all other higher rank Lie groups, except possibly $\mathrm{SL}_{2n+1}(\mathbb{R})$, $\mathrm{SL}_{2n+1}(\mathbb{C})$, $\mathrm{SL}_n(\mathbb{H})$, or groups of type $E_6$.
