论文标题
$ k $ - 非交换性伯努利班次的理论
$K$-theory of non-commutative Bernoulli Shifts
论文作者
论文摘要
对于一大批C*-Algebras $ a $，我们计算了$ k $ - 减少的交叉产品的理论$ a^{\ otimes g} \ rtimes_rg $ bernoulli的ber um-connes猜测。特别是，我们给出了有限维c*代数，UHF-Elgebras，旋转代数和其他几个示例的明确公式。作为一个应用程序，我们获得了$ k $的公式，包括$ k $的理论，包括花圈产品的c* - 代数$ h \ wr g $，用于$ h $和$ g $的大型类别。我们的方法使用第二名作者与Joachim Cuntz和Xin li一起开发的技术的概括，以及对UHF代数有限群体动作的微不足道定理，由第三和第四名的作者在同伴论文中开发。
For a large class of C*-algebras $A$, we calculate the $K$-theory of reduced crossed products $A^{\otimes G}\rtimes_rG$ of Bernoulli shifts by groups satisfying the Baum--Connes conjecture. In particular, we give explicit formulas for finite-dimensional C*-algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the $K$-theory of reduced C*-algebras of wreath products $H\wr G$ for large classes of groups $H$ and $G$. Our methods use a generalization of techniques developed by the second named author together with Joachim Cuntz and Xin Li, and a trivialization theorem for finite group actions on UHF algebras developed in a companion paper by the third and fourth named authors.
