论文标题
与完成两分图相关的2级图的C* - 代数的K理论
The K-theory of the C*-algebras of 2-rank graphs associated to complete bipartite graphs
论文作者
论文摘要
使用Vdovina的结果，我们可以与每个完整的连接的两部分图$κ$ a $ 2 $二维的正方形复合体相关联，我们称之为瓷砖复合物，每个顶点的链接为$κ$。我们以两种不同的方式将瓷砖复合物视为$ 2 $ rank图。对于每个$ 2 $ -LANK图，我们都关联了一个通用的C*-Algebra，我们为其计算K理论，从而提供了带有显式k-groups的$ 2 $ -LANK图代数的新无限集合。我们确定瓷砖复合物的同源性，并将程序概括为由侧面数量较高的多边形组成的复合物和系统。
Using a result of Vdovina, we may associate to each complete connected bipartite graph $κ$ a $2$-dimensional square complex, which we call a tile complex, whose link at each vertex is $κ$. We regard the tile complex in two different ways, each having a different structure as a $2$-rank graph. To each $2$-rank graph is associated a universal C*-algebra, for which we compute the K-theory, thus providing a new infinite collection of $2$-rank graph algebras with explicit K-groups. We determine the homology of the tile complexes, and give generalisations of the procedures to complexes and systems consisting of polygons with a higher number of sides.
