论文标题
C* - 作用于建筑物的组的高级图的代数，并明确计算其K理论
C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory
论文作者
论文摘要
我们将类别理论，K理论和几何组理论的要素结合起来，定义一个称为$ k $ -cube群体的组，这些组对$ k $ trees的乘积进行自由和过渡性，以任意$ k $。此动作对树木产物的商人定义了$ k $尺寸的立方体复合体，该综合体诱发了更高的图形。我们对相应的$ k $ -rank Graph c*-Algebras的K理论进行推论，并提供$ K $ -Cube组及其K理论的明确示例。我们为$ k \ geq 3 $的无限家族提供了k理论的明确计算，这不是张张量产品的künneth定理的直接结果。
We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action on the product of trees defines a $k$-dimensional cube complex, which induces a higher-rank graph. We make deductions about the K-theory of the corresponding $k$-rank graph C*-algebras, and give explicit examples of $k$-cube groups and their K-theory. We give explicit computations of K-theory for an infinite family of $k$-rank graphs for $k\geq 3$, which is not a direct consequence of the Künneth Theorem for tensor products.
