论文标题
$ C^*$ - 半群动力学系统的信封和扩张理论
$C^*$-Envelope and Dilation Theory of Semigroup Dynamical Systems
论文作者
论文摘要
在本文中，我们为某些类别的半群动力系统构建了两个操作员代数，它们相对于它们相应的协方差条件是普遍的：一个是自我偶像，另一个是非自我偶像。我们证明，非自助接合操作员代数的$ c^*$ - 完全是自我偶像。该结果导致了许多新的操作员代数及其$ c^*$ - 信封的新示例，其中许多来自数字字段和通勤环。我们进一步建立了这些操作员代数的功能及其应用。
In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being self-adjoint, and another being non-self-adjoint. We prove that the $C^*$-envelope of the non-self-adjoint operator algebra is precisely the self-adjoint one. This result leads to a number of new examples of operator algebras and their $C^*$-envelopes, with many from number fields and commutative rings. We further establish the functoriality of these operator algebras along with their applications.
