论文标题
从图形的长度放置下降到图代数的一余次回调
From length-preserving pushouts of graphs to one-surjective pullbacks of graph algebras
论文作者
论文摘要
有向图的工会是有向图的推翻的最简单示例。他们违反的条件诱导了图表C* - 代数的溢流量规等值回调，并在非交通性拓扑（例如量子球和球体）中进行了充分的研究并进行了大量实例化。在此，我们超越了图的工会，以系统地确定图形的更一般长度可呈现的下推动的最佳条件，在这些条件下，它们违反了路径代数，Leavitt路径代数和图形C*-Algebras的分级回调。正如自然示例和K理论所决定的，我们的回调仅在一侧过渡。提出的新方法将应用程序的范围从可接受的子图（也称为商图）扩大到插座的未标记折叠的概括，并将图形的线图折叠到初始图。此外，我们介绍了本地派生的图的概念，该图实质上扩展了派生图的范式（或图形的偏斜产物），并使用从局部派生的图的投影折叠到其基础（或电压）图以获得图形C*-Algebras的单位缩放。
The unions of directed graphs are the simplest examples of pushouts of directed graphs. The conditions under which they contravariantly induce surjective gauge-equivariant pullbacks of graph C*-algebras have been well studied and vastly instantiated in noncommutative topology (e.g., quantum balls and spheres). Herein, we go beyond the unions of graphs to systematically determine optimal conditions for more general length-preserving pushouts of graphs under which they contravariantly induce graded pullbacks of path algebras, Leavitt path algebras, and graph C*-algebras. Our pullbacks are surjective only on one side, as dictated by natural examples and K-theory. The proposed new approach enlarges the scope of applications from admissible subgraphs (also called quotient graphs) to generalizations of unlabeled foldings of Stallings and collapsing the line graphs of graphs to initial graphs. Moreover, we introduce the concept of locally derived graphs, which substantially extends the paradigm of derived graphs (or skew products of graphs), and use the projection foldings from locally derived graphs to their base (or voltage) graphs to obtain one-surjective pullbacks of graph C*-algebras.
