论文标题
右角建筑物通用群体的拓扑和代数特性
Topological and algebraic properties of universal groups for right-angled buildings
论文作者
论文摘要
我们研究右角建筑物的通用团体。受西蒙·史密斯（Simon Smith）在树木的通用群体上的工作的启发，我们明确允许不一定是有限或及时性的本地群体。我们在此扩展环境中讨论各种拓扑和代数属性。特别是，我们表征了这些组何时在本地紧凑的情况下，何时抽象地简单，何时它们原始作用于建筑物的残基，并且我们讨论了一些必要的和足够的条件，以使各组被紧凑。 我们指出，与这些建筑物的几何形状和图表相关的意外方面，这些建筑影响相应通用群体的拓扑和代数特性。
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and algebraic properties in this extended setting. In particular, we characterise when these groups are locally compact, when they are abstractly simple, when they act primitively on residues of the building, and we discuss some necessary and sufficient conditions for the groups to be compactly generated. We point out that there are unexpected aspects related to the geometry and the diagram of these buildings that influence the topological and algebraic properties of the corresponding universal groups.
