标题： 左可消去半群的C$^*$-代数的边界商及其群胚模型 显示英文标题

标题： Boundary quotients of C$^*$-algebras of left cancellative monoids and their groupoid models

摘要： 对于一个左可消去的独异点$S$，我们考虑其约化半群 C$^*$-代数$C_r^*(S)$的一个商，称为边界商。 我们提出了这两种可能的群胚模型，作为与$S$相关的 Paterson 和 Spielberg 群胚的约化，并制定了关于$S$的条件，以保证其中任何一个是一个群胚模型。 我们概述了这些条件与之前论文中引入的（强）C$^*$-正则性的概念之间的关系，并构造了一个左可消去的独异点的例子，该独异点不是 C$^*$-正则的，但满足这两个新条件。 显示英文摘要

摘要： For a left cancellative monoid $S$ we consider a quotient of the reduced semigroup C$^*$-algebra $C_r^*(S)$ known as the boundary quotient. We present two potential groupoid models for this boundary quotient, obtained as reductions of Paterson and Spielberg's groupoids associated to $S$, and formulate conditions on $S$ which guarantees that either is a groupoid model. We outline how these conditions are related to the notions (strong) C$^*$-regularity introduced in a previous paper, and construct an example of a left cancellative monoid which is not C$^*$-regular, but satisfies both of the new conditions.