由作用于建筑的群产生的高秩图C*-代数及其K-理论的显式计算
C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory
AI总结：
本文通过定义k-立方体群并利用其作用于树乘积的商构造高秩图，进而研究相应C*-代数的K-理论，并对k≥3的无限族给出非Künneth定理直接推论的显式计算。
摘要：
我们通过定义一类称为k-立方体群的群，将范畴论、K-理论和几何群论的元素结合起来，这类群对任意k自由且传递地作用于k棵树的乘积上。该作用在树的乘积上的商定义了一个k维立方体复形，它诱导出一个高秩图。我们对相应的k-秩图C*-代数的K-理论作出推导，并给出k-立方体群及其K-理论的显式例子。我们对k≥3的一族无限多个k-秩图给出K-理论的显式计算，这不是张量积的Künneth定理的直接推论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
