Crossed products of C ∗ -algebras C(X,A) and their applications
Crossed products of C ∗ -algebras C(X,A) and their applications
复制标题
C→代数C(X,A)的叉积及其应用
DOI：
10.1142/s0129167x16500294
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发表时间：
2016
影响因子：
0.6
通讯作者：
花家杰
中科院分区：
文献类型：
--
作者：
花家杰
Let $X$ be an infinite compact metric space with finite covering dimension, let $A$ be a unital separable simple AH-algebra with no dimension growth,.and denote by $C(X,A)$ the $C^*$-algebra of all continuous functions from.$X$ to $A.$ Suppose that $\gamma:\mathbb{Z}^{d}\rightarrow {\rm Aut}(C(X,A))$ is a minimal group action and the induced $\mathbb{Z}^{d}$-action on $X$ is free. Under certain conditions, we show the crossed product $C^*$-algebra $C(X,A)\rtimes_{\gamma} \mathbb{Z}^d$ has rational tracial rank zero and hence is classified by its Elliott invariant..Next, we show the following: Let $Y$ be a Cantor set, let $A$ be a stably finite unital separable simple $C^*$-algebra which is rationally TA$\mathcal{S},$ where $\mathcal{S}$ is a class of separable unital $C^*$-algebras which is closed under tensoring with finite dimensional $C^*$-algebras and closed under taking unital.hereditary sub-$C^*$-algebras,.and let $\alpha\in {\rm Aut}(C(Y,A))$..Under certain conditions, we conclude that $C(Y,A)\rtimes_{\alpha}\mathbb{Z}$ is rationally TA$\mathcal{S}.$.Finally, we classify the crossed products of certain unital simple $C^*$-algebras by using the crossed products of $C(Y,A)$.
Let $X$ be an infinite compact metric space with finite covering dimension, let $A$ be a unital separable simple AH-algebra with no dimension growth,.and denote by $C(X,A)$ the $C^*$-algebra of all continuous functions from.$X$ to $A.$ Suppose that $\gamma:\mathbb{Z}^{d}\rightarrow {\rm Aut}(C(X,A))$ is a minimal group action and the induced $\mathbb{Z}^{d}$-action on $X$ is free. Under certain conditions, we show the crossed product $C^*$-algebra $C(X,A)\rtimes_{\gamma} \mathbb{Z}^d$ has rational tracial rank zero and hence is classified by its Elliott invariant..Next, we show the following: Let $Y$ be a Cantor set, let $A$ be a stably finite unital separable simple $C^*$-algebra which is rationally TA$\mathcal{S},$ where $\mathcal{S}$ is a class of separable unital $C^*$-algebras which is closed under tensoring with finite dimensional $C^*$-algebras and closed under taking unital.hereditary sub-$C^*$-algebras,.and let $\alpha\in {\rm Aut}(C(Y,A))$..Under certain conditions, we conclude that $C(Y,A)\rtimes_{\alpha}\mathbb{Z}$ is rationally TA$\mathcal{S}.$.Finally, we classify the crossed products of certain unital simple $C^*$-algebras by using the crossed products of $C(Y,A)$.