论文标题
右角建筑物的限制性群体
Restricted universal groups for right-angled buildings
论文作者
论文摘要
2000年，马克·伯格（Marc Burger）和沙哈尔·莫兹斯（Shahar Mozes）引入了行动在树木上的普遍团体。这样的组提供了完全断开局部紧凑型组的有趣示例。直观地，这些是所有地方行动都满足规定行为的最大群体。 从那时起，他们的研究就在各个方向发展。特别是，Adrien Le Boudec研究了受限制的通用群体，在这些群体中，规定的行为被允许在有限数量的顶点中违反。另一方面，我们一直在研究作用于右角建筑物的通用群体，这是一类比树木更通用的几何对象。 当前论文的目的是结合这两个想法：我们将研究对右角建筑物作用的受限制的通用群体。我们显示了这些组的几个排列和拓扑特性，主要结果是这些组简单的确切标准。
In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitively, these are the largest groups for which all local actions satisfy a prescribed behavior. Since then, their study has evolved in various directions. In particular, Adrien Le Boudec has studied restricted universal groups, where the prescribed behavior is allowed to be violated in a finite number of vertices. On the other hand, we have been studying universal groups acting on right-angled buildings, a class of geometric objects with a much more general structure than trees. The aim of the current paper is to combine both ideas: we will study restricted universal groups acting on right-angled buildings. We show several permutational and topological properties of those groups, with as main result a precise criterion for when these groups are simple.
