论文标题
可以计算完全断开的本地紧凑型组
Computably totally disconnected locally compact groups
论文作者
论文摘要
我们从算法的角度研究了完全断开的局部紧凑（T.D.L.C.）组。我们提供了各种方法来定义T.D.L.C. \组的可计算表现，并显示它们的等效性。在此过程中，我们获得了T.D.L.C.〜组与紧凑型开放式coset给出的某些可计数有序的群体之间的算法石型二元性。我们利用这些不同方法给出的灵活性，以表明几个自然组，例如$ \ aut（t_d）$和$ \ sl_n（\ qq_p）$，具有可计算的演示文稿。我们表明，从T.D.L.C. \组到新的T.D.L.C. \组的许多结构都具有算法版本，这些版本保留在计算出呈现的T.D.L.C. \组的类别中。这将导致进一步的示例，例如$ \ pgl_n（\ qq_p）$。我们研究与T.D.L.C. \ cluctable Companiage相关的对象是否可计算：在紧凑型情况下，模块化函数，比例函数和Cayley-Abels图。当T.D.L.C.〜组的可计算演示文稿是唯一的可计算同构，并将其应用于$ \ QQ_P $作为添加剂组，而半领产品$ \ zz \ ltimes \ qq_p $，我们给出了标准。我们给（与威利斯联合）一个计算的T.D.L.C.具有不可归结的比例功能的组。
We study totally disconnected, locally compact (t.d.l.c.) groups from an algorithmic perspective. We give various approaches to defining computable presentations of t.d.l.c.\ groups, and show their equivalence. In the process, we obtain an algorithmic Stone-type duality between t.d.l.c.~groups and certain countable ordered groupoids given by the compact open cosets. We exploit the flexibility given by these different approaches to show that several natural groups, such as $\Aut(T_d)$ and $\SL_n(\QQ_p)$, have computable presentations. We show that many construction leading from t.d.l.c.\ groups to new t.d.l.c.\ groups have algorithmic versions that stay within the class of computably presented t.d.l.c.\ groups. This leads to further examples, such as $\PGL_n(\QQ_p)$. We study whether objects associated with computably t.d.l.c.\ groups are computable: the modular function, the scale function, and Cayley-Abels graphs in the compactly generated case. We give a criterion when computable presentations of t.d.l.c.~groups are unique up to computable isomorphism, and apply it to $\QQ_p$ as an additive group, and the semidirect product $\ZZ\ltimes \QQ_p$. We give (joint with Willis) an example of a computably t.d.l.c. group with noncomputable scale function.
