K-Theory of Crossed Products of Tiling C*-Algebras by Rotation Groups
K-Theory of Crossed Products of Tiling C*-Algebras by Rotation Groups
复制标题
旋转群平铺C*-代数的叉积的K理论
DOI：
10.1007/s00220-014-2070-5
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发表时间：
2013
影响因子：
2.4
通讯作者：
Charles Starling
中科院分区：
文献类型：
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作者：
Charles Starling
设Ω是一个平铺空间，G是使Ω不动的极大旋转群.因此Ω的上同调和Ω/G都是不变量，它们给出了Ω中镶嵌的有用几何信息。Ω的上同调的非交换类似物是与Ω相关联的C *-代数的K-理论，并且对于维数为2或更小的有限平铺，K-理论同构于上同调群的直和。本文给出了计算Ω/G的上同调的非交换模拟的一个公式，即拼接C~*-代数与G的交叉积的K-理论。我们还提供了一个表格，其中包含许多常见示例的一些计算K群，包括彭罗斯和风车平铺。
Let Ω be a tiling space and let G be the maximal group of rotations which fixes Ω. Then the cohomology of Ω and Ω/G are both invariants which give useful geometric information about the tilings in Ω. The noncommutative analog of the cohomology of Ω is the K-theory of a C*-algebra associated to Ω, and for translationally finite tilings of dimension 2 or less, the K-theory is isomorphic to the direct sum of cohomology groups. In this paper we give a prescription for calculating the noncommutative analog of the cohomology of Ω/G, that is, the K-theory of the crossed product of the tiling C*-algebra by G. We also provide a table with some calculated K-groups for many common examples, including the Penrose and pinwheel tilings.