论文标题
与$ \ mathbb {n}^{k} $ -actions相关的某些classoids上的cocycles
Cocycles on Certain Groupoids Associated to $ \mathbb{N}^{k} $-Actions
论文作者
论文摘要
我们考虑通过在紧凑型公制空间上作用的局部同构的有限通勤同态构建的类固醇，并研究了与这些群体相关的$ c^{\ ast} $ algebras的$ c^{\ ast} $ algebras。我们在这些群体上以$ 1 $ cocycles的形式提供新的表征，以当地紧凑的Abelian群体的价值，以$ k $的$ k $ - thupllass在单位空间上的连续功能表示满足某些规范身份。使用它，我们为几个通勤操作员的动态系统（$ k $ -ruelle-ruelle Trielles and vissing Ruelle运营商）开发了扩展的Ruelle-Perron-Frobenius理论。在$ c^{\ ast} $ -Algebras上，从这些群体构建的$ c^{\ ast}上的结果。当研究的类固醇来自较高的图表时，我们的结果恢复了与图形相关的KMS状态的存在 - 唯一性结果。
We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{\ast} $-algebras associated to these groupoids. We provide a new characterization of $ 1 $-cocycles on these groupoids taking values in a locally compact abelian group, given in terms of $ k $-tuples of continuous functions on the unit space satisfying certain canonical identities. Using this, we develop an extended Ruelle-Perron-Frobenius theory for dynamical systems of several commuting operators ($ k $-Ruelle triples and commuting Ruelle operators). Results on KMS states on $ C^{\ast} $-algebras constructed from these groupoids are derived. When the groupoids being studied come from higher-rank graphs, our results recover existence-uniqueness results for KMS states associated to the graphs.
