仿射建筑物的边界共不变量和K理论中的挠率
Torsion in Boundary Coinvariants and K-theory for Affine Buildings
摘要：
设$(G,{\mathfrak I},N,S)$是仿射拓扑Tits系统，$Γ$是$G$中的无挠余紧格.本文研究了共不变量$H_0(Γ; C(Ω,{\mathbb Z}))$，其中$Ω$是$G$的Furstenberg边界.证明了$H_0(Γ; C(Ω,{\mathbb Z}))$中的恒等函数类$[1]$具有有限阶，且阶有明确的界.类似的陈述适用于边界交叉积$C^*$ -代数$C(Ω)\rtimesΓ$的$K_0$群。当Tits系统具有$\widetilde A_2$型时，给出了交叉积代数和约化群$C^*$ -代数的精确计算.
英文摘要：
Let $(G,{\mathfrak I},N,S)$ be an affine topological Tits system, and let $Γ$ be a torsion free cocompact lattice in $G$. This article studies the coinvariants $H_0(Γ; C(Ω,{\mathbb Z}))$, where $Ω$ is the Furstenberg boundary of $G$. It is shown that the class $[1]$ of the identity function in $H_0(Γ; C(Ω,{\mathbb Z}))$ has finite order, with explicit bounds for the order. A similar statement applies to the $K_0$ group of the boundary crossed product $C^*$-algebra $C(Ω)\rtimesΓ$. If the Tits system has type $\widetilde A_2$, exact computations are given, both for the crossed product algebra and for the reduced group $C^*$-algebra.
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。
