论文标题
代数动作I. C* - 代数和群体
Algebraic actions I. C*-algebras and groupoids
论文作者
论文摘要
我们提供了一个框架，用于研究与半群的代数作用相关的混凝土C*代数：鉴于这样的作用，我们构建了一个反向半群，并且我们引入了代数作用的条件，以表征hausdorffness，拓扑效率和相关紧密组的最低限度。我们将我们群体的单位空间的所有闭合不变子空间参数化，并表征相关还原类固醇的拓扑界。我们证明，每当它们最小的情况下，我们的类固醇是纯粹的无限，在拓扑上，我们证明我们的混凝土C*-Algebra始终是（可能是异国情调的）群体c*-algebra，因为它位于我们群体的完整和必需的C*-Essential c* - 我们群体的c*-ergebras之间。作为一种应用，我们获得了与类似的c* - 代数相关的结构性结果，例如，对半群的转变，来自交换代数的动作和非交通戒指。
We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce conditions for algebraic actions that characterize Hausdorffness, topological freeness, and minimality of the associated tight groupoid. We parameterize all closed invariant subspaces of the unit space of our groupoid, and characterize topological freeness of the associated reduction groupoids. We prove that our groupoids are purely infinite whenever they are minimal, and in the topologically free case, we prove that our concrete C*-algebra is always a (possibly exotic) groupoid C*-algebra in the sense that it sits between the full and essential C*-algebras of our groupoid. As an application, we obtain structural results for C*-algebras associated with, for instance, shifts over semigroups, actions coming from commutative algebra, and non-commutative rings.
