Non-commutative shifts and crossed products
Non-commutative shifts and crossed products
复制标题
非交换移位和交叉积
DOI：
10.1016/s0022-1236(03)00024-7
复制
发表时间：
2003
影响因子：
1.7
通讯作者：
A. Kishimoto
中科院分区：
文献类型：
--
作者：
A. Kishimoto
当A是一元简单AF C * -代数且具有唯一迹态时，证明了两侧无限张量积⊗ZA与位移的交叉积是一个迹迹AF C * -代数。对于某非单无穷张量与平移的交叉积，也给出了类似的结果。利用H. Lin对这类C * -代数的一个意义深远的分类结果，我们得到了一个非近似内的AF C * -代数上的单参数自同构群的一个例子，即所谓的幂- sakai猜想[23]的AF版本的一个反例。
When A is a unital simple AF C∗-algebra and has a unique tracial state, it is shown that the crossed product of the two-sided infinite tensor product ⊗ZA by the shift is a tracially AF C∗-algebra. A similar result is given to the crossed product of a certain non-unital two-sided infinite tensor product by the shift. Applying a far-reaching classification result of such C∗-algebras by H. Lin, we obtain an example of a one-parameter automorphism group on some AF C∗-algebra which is not approximately inner, a counter-example to the AF version of the so-called Powers–Sakai conjecture [23].