A generalized Powers averaging property for commutative crossed products
Tattwamasi Amrutam, Dan Ursu
备注：
24 pages; To appear in Transactions of the American Mathematical Society. This is the accepted manuscript, which includes all changes requested by the referee
发表信息：
Transactions of the American Mathematical Society 375 (2022), no. 3, 2237-2254
We prove a generalized version of Powers' averaging property that characterizes simplicity of reduced crossed products $C(X) \rtimes_λG$, where $G$ is a countable discrete group, and $X$ is a compact Hausdorff space which $G$ acts on minimally by homeomorphisms. As a consequence, we generalize results of Hartman and Kalantar on unique stationarity to the state space of $C(X) \rtimes_λG$ and to Kawabe's generalized space of amenable subgroups $\operatorname{Sub}_a(X,G)$. This further lets us generalize a result of the first named author and Kalantar on simplicity of intermediate C*-algebras. We prove that if $C(Y) \subseteq C(X)$ is an inclusion of unital commutative $G$-C*-algebras with $X$ minimal and $C(Y) \rtimes_λG$ simple, then any intermediate C*-algebra $A$ satisfying $C(Y) \rtimes_λG \subseteq A \subseteq C(X) \rtimes_λG$ is simple.
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Unique equivariant pseudo expectation and generalized Powers averaging for crossed product
Institute of Mathematics of the Polish Academy of Sciences（波兰科学院数学研究所）；University of Isfahan（伊斯法罕大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Alzahra University（阿尔扎拉大学）
We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no proper non-trivial invariant ideals, and the reduced crossed product has a unique tracial state if and on…
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The C$^*$-envelope of a semicrossed product and Nest Representations
设$X$是紧Hausdorff，$ϕ: X \to X$是连续满射.设$\mathcal{A}$是对应于关系fU = UfPDMATHABMP $ or to the relation $ Uf = f \circ U的半交叉积代数. $ Then the C$ ^* $-envelope of $ \mathcal{A} $ is the crossed product of a commutative C$ ^* $-algebra which contains $ C（X）$作为一个子代数，关于我们构造的同胚。我们还表明，有“足够多”的巢表示。
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