We show how to construct a family of groups with simple commutator subgroups from aperiodic 1-vertex, finitely aligned higher rank graphs (which are, in fact, a class of cancellative monoids). Inverse semigroups form the intermediary between these cancellative monoids and the family of groups we are interested in. These groups can naturally be viewed as higher-dimensional generalizations of the classical Thompson groups since the finite direct products of free monoids are examples of the appropriate 1-vertex higher rank graphs.

中文翻译：

---

汤普森群的高维推广

我们展示了如何从非周期性 1 顶点、有限对齐的高阶图（实际上是一类取消幺半群）构造具有简单交换子子群的群族。逆半群形成了这些可取消的幺半群和我们感兴趣的群族之间的中介。这些群自然可以被视为经典 Thompson 群的高维推广，因为自由幺半群的有限直积是适当的 1-顶点高秩图。