Crossed products by finite group actions with the Rokhlin property
Crossed products by finite group actions with the Rokhlin property
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DOI：
10.1007/s00209-010-0784-4
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发表时间：
2011-04
影响因子：
0.8
通讯作者：
H. Osaka;N. Phillips
中科院分区：
文献类型：
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作者：
H. Osaka;N. Phillips
我们证明了一些类的可分单位C*-代数在具有Rokhlin性质的有限群作用的交叉积下是封闭的，包括：（a）AI代数，AT代数，以及相关的类，其特征在于使用半投射构建块的直接极限分解。(b)维数增长缓慢且真实的秩为零的单酉AH代数。(c)具有真实的秩为零或稳定秩为一的C*-代数。(d)单C*-代数，其投影的阶由迹决定。(e)C*-代数的幂等元都满足泛系数定理。(f)具有唯一迹状态的C*-代数。沿着的方式，我们给出了一个系统的治疗，从局部逼近条件的同态图像，不一定是内射的直接极限分解的推导。
We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective.