Partial Transformation Groupoids Attached to Graphs and Semigroups
Partial Transformation Groupoids Attached to Graphs and Semigroups
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附加到图和半群的部分变换群形
DOI：
10.1093/imrn/rnw166
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发表时间：
2016
影响因子：
1
通讯作者：
Li X
中科院分区：
文献类型：
--
作者：
Li X
引入了部分动力系统连续轨道等价的概念，并给出了部分C*-交叉积的Cartan同构的等价刻画。图C ~*-代数和半群C ~*-代数都可以描述为附着在部分动力系统上的C ~*-代数。作为应用，对于图，我们推广和解释了松本和Matui关于轨道等价和Cartan同构的一个结果;对于半群，我们加强了半群C*-代数关于边界条件的顺从性、核性和单性的几个结构性结果.我们还讨论了由图和半群产生的部分变换群胚的纯无限性。
We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras can be described as C*-algebras attached to partial dynamical systems. As applications, for graphs, we generalize and explain a result of Matsumoto and Matui relating orbit equivalence and Cartan-isomorphism, and for semigroups, we strengthen several structural results for semigroup C*-algebras concerning amenability, nuclearity as well as simplicity of boundary quotients. We also discuss pure infiniteness for partial transformation groupoids arising from graphs and semigroups.