标题： 比较理论和光滑最小C*-动力学 显示英文标题

标题： Comparison theory and smooth minimal C*-dynamics

摘要： 我们证明了最小微分同胚的C*-代数满足正元素的Blackadar基本可比较性性质。这导致了在K理论和迹的基础上对这类代数上可数生成的Hilbert模的同构类进行分类，以及对自伴元的单位轨道闭包的类似分类。我们还得到了这种情况下Cuntz半群的结构定理，并证明了Blackadar和Handelman的猜想：下半连续维函数在所有维函数的空间中是弱稠的。这些结果在更广泛的单位单ASh代数设置中仍然成立，这些代数具有缓慢维数增长和稳定秩一。我们的主要工具是对递归子齐次C*-代数的比较半径的一个精确界限。这也用于构造不可数多个非Morita等价的简单可分的阿贝尔C*-代数，它们具有相同的K理论和迹状态空间，提供了McDuff的II_1因子不可数族的C*-代数类似物。我们顺便证明了比较半径的范围被简单C*-代数所耗尽。 显示英文摘要

摘要： We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's uncountable family of II_1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.