论文标题
移动$ k $ - 图保存莫里塔等价
Moves on $k$-graphs preserving Morita equivalence
论文作者
论文摘要
我们启动程序，将有向图的几何分类扩展到高级图（$ k $ -graphs），该程序在2016年《 Eilers》，《雷斯托夫》，ruiz和sorensen [errs16]中完成了有向图$ c^*$ - 代数的几何分类。确切地说，我们确定了四个“移动”或修改，一个人可以在$ k $ -graph $λ$上执行，这会使其$ c^*$ - 代数$ c^*（λ）$不变。这些动作 - 隔离，延迟，下沉的删除和还原 - 灵感来自Sorensen [S \ O13]和Bates-Pask [BP04]所描述的有向图的动作。因此，我们对$ k $ graphs的看法集中在基本的有向图上。因此，我们包括两个新的结果定理2.3和引理2.9，涉及$ k $ graph及其基础有向图之间的关系。
We initiate the program of extending to higher-rank graphs ($k$-graphs) the geometric classification of directed graph $C^*$-algebras, as completed in the 2016 paper of Eilers, Restorff, Ruiz, and Sorensen [ERRS16]. To be precise, we identify four "moves," or modifications, one can perform on a $k$-graph $Λ$, which leave invariant the Morita equivalence class of its $C^*$-algebra $C^*(Λ)$. These moves -- insplitting, delay, sink deletion, and reduction -- are inspired by the moves for directed graphs described by Sorensen [S\o13] and Bates-Pask [BP04]. Because of this, our perspective on $k$-graphs focuses on the underlying directed graph. We consequently include two new results, Theorem 2.3 and Lemma 2.9, about the relationship between a $k$-graph and its underlying directed graph.
