论文标题
跨产品的分类性分类
Classifiability of crossed products by nonamenable groups
论文作者
论文摘要
我们表明，在紧凑的度量空间上，大量不可统的可计数基团的所有可及时的，最小的作用都具有动态比较。该课程包括所有不符合的双曲线组，许多HNN延伸，不可纳的baumslag-solitar群组，一大批合并的免费产品，许多Lie组的格子，$ \ wideTilde {a} _2 _2 $ - 群体，以及上面的产品，以及与自由计算可计录的群体的直接产品。结果，这些群体在紧凑型公制空间上的amenable，最小和拓扑上的跨产品是UCT类中的Kirchberg代数，因此由$ k $ - 理论进行了分类。
We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable Baumslag-Solitar groups, a large class of amalgamated free products, lattices in many Lie groups, $\widetilde{A}_2$-groups, as well as direct products of the above with arbitrary countable groups. As a consequence, crossed products by amenable, minimal and topologically free actions of such groups on compact metric spaces are Kirchberg algebras in the UCT class, and are therefore classified by $K$-theory.
