置换平铺C* 代数上的有限对称群作用
Finite symmetry group actions on substitution tiling C*-algebras
摘要：
对于非周期置换镶嵌系统$(\p,ω)$的有限对称群$G$，证明了镶嵌C* 代数$\Aw$与$G$的交叉积具有实秩零、迹秩1和唯一迹，且其K-理论的阶由迹决定.证明了$G$在$\Aw$上的作用满足弱Rokhlin性质，并且只要$\Aw$的迹秩为零，它也满足迹Rokhlin性质.在证明后者的过程中，我们证明了$\Aw$是可生成的。我们还提供了一个链接之间的$\Aw$和AF代数Connes相关的彭罗斯镶嵌。
英文摘要：
For a finite symmetry group $G$ of an aperiodic substitution tiling system $(\p,ω)$, we show that the crossed product of the tiling C*-algebra $\Aw$ by $G$ has real rank zero, tracial rank one, a unique trace, and that order on its K-theory is determined by the trace. We also show that the action of $G$ on $\Aw$ satisfies the weak Rokhlin property, and that it also satisfies the tracial Rokhlin property provided that $\Aw$ has tracial rank zero. In the course of proving the latter we show that $\Aw$ is finitely generated. We also provide a link between $\Aw$ and the AF algebra Connes associated to the Penrose tilings.
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