PARTIAL DYNAMICAL SYSTEMS AND C -ALGEBRAS GENERATED BY PARTIAL ISOMETRIES
PARTIAL DYNAMICAL SYSTEMS AND C -ALGEBRAS GENERATED BY PARTIAL ISOMETRIES
复制标题
部分动力系统和由部分等轴测图生成的 C 代数
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
John Quigg
中科院分区：
文献类型：
--
作者：
R. Exel;Marcelo Laca;John Quigg
其范围和初始投影满足一组指定条件的部分等距集合通常会产生一个群体的部分表示。因此，相应的 C 代数是群的部分表示的通用 C 代数的商，通过群的部分作用，它从群中继承了阿贝尔 C 代数的交叉积结构。这使我们能够表征忠实的表示和简单性，并根据相关部分作用的顺从性和拓扑自由度来研究这些 C 代数的理想结构。我们还考虑了三个具体应用：群的部分表示、准格有序群的 Toeplitz 代数以及 Cuntz-Krieger 代数。
A collection of partial isometries whose range and initial pro- jections satisfy a specified set of conditions often gives rise to a partial rep- resentation of a group. The corresponding C -algebra is thus a quotient of the universal C -algebra for partial representations of the group, from which it inherits a crossed product structure, of an abelian C -algebra by a partial action of the group. This allows us to characterize faithful representations and simplicity, and to study the ideal structure of these C -algebras in terms of amenability and topological freeness of the associated partial action. We also consider three specific applications: to partial representations of groups, to Toeplitz algebras of quasi-lattice ordered groups, and to Cuntz-Krieger algebras.