CROSSED PRODUCTS OF CERTAIN C*-ALGEBRAS
CROSSED PRODUCTS OF CERTAIN C*-ALGEBRAS
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DOI：
10.1142/s0129167x14500104
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发表时间：
2014-03
影响因子：
0.6
通讯作者：
Jiajie Hua;Yan Wu
中科院分区：
文献类型：
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作者：
Jiajie Hua;Yan Wu
设X是Cantor集，A是有理迹秩不超过1的有单位可分单顺从稳定C*-代数，满足泛系数定理（UCT）.我们用C（X，A）表示从X到A的所有连续函数的代数。设α是C（X，A）上的自同构.设C（X，A）是α-单的，[α| 1 A] = [id| 1 A]在KL（1 <$A，C（X，A）），τ（α（1 <$a））= τ（1 <$a），对所有τ ∈ T（C（X，A））和所有a ∈ A，对所有u ∈ U（A）（其中α和id分别是由α和id诱导的从U（C（X，A））/CU（C（X，A））→ U（C（X，A））/CU（C（X，A））的同态，并且其中CU（C（X，A））A））是C（X，A））的酉群U（C（X，A））的乘子生成的子群的闭包，则相应的交叉积C（X，A）<$α <$是有理迹秩不大于1的有单位的单稳定C*-代数，满足UCT.设X是一个康托集，X是一个圆。设γ：X× n → X× n是极小同胚.证明了只要上圈是旋转的，相应的交叉积C*-代数的迹秩总是不大于1。
Let X be a Cantor set, and let A be a unital separable simple amenable -stable C*-algebra with rationally tracial rank no more than one, which satisfies the Universal Coefficient Theorem (UCT). We use C(X, A) to denote the algebra of all continuous functions from X to A. Let α be an automorphism on C(X, A). Suppose that C(X, A) is α-simple, [α|1⊗A] = [id|1⊗A] in KL(1 ⊗ A, C(X, A)), τ(α(1 ⊗ a)) = τ(1 ⊗ a) for all τ ∈ T(C(X, A)) and all a ∈ A, and for all u ∈ U(A) (where α‡ and id‡ are homomorphisms from U(C(X, A))/CU(C(X, A)) → U(C(X, A))/CU(C(X, A)) induced by α and id, respectively, and where CU(C(X, A)) is the closure of the subgroup generated by commutators of the unitary group U(C(X, A)) of C(X, A)), then the corresponding crossed product C(X, A) ⋊α ℤ is a unital simple -stable C*-algebra with rationally tracial rank no more than one, which satisfies the UCT. Let X be a Cantor set and 𝕋 be the circle. Let γ : X × 𝕋n → X × 𝕋n be a minimal homeomorphism. It is proved that, as long as the cocycles are rotations, the tracial rank of the corresponding crossed product C*-algebra is always no more than one.