湍流、轨道等价与核C* 代数的分类
Turbulence, orbit equivalence, and the classification of nuclear C*-algebras
摘要：
本文给出了核单可分C* 代数-代数同构关系的Borel基数的界：它是动荡的，但Borel可约化为Cuntz代数O_2的自同构群在其闭子集上的作用.对可度量化的Choquet单形的仿射同胚也得到了同样的界。作为一个副产品，我们恢复Kechris和Solecki的结果，即，在希尔伯特立方体的同胚的Recta是Borel可约化的波兰群作用。这些结果与核单C* 代数-代数的K-理论和迹的分类理论密切相关。为了进一步研究C* 代数-代数的Borel复杂性，证明了许多标准的C* 代数-代数的构造和关系都是Borel的，并证明了Kirchberg的O_2-稳定性和嵌入定理的Borel版本。我们还找到了K_σ硬等价关系的C*-代数证明.
英文摘要：
We bound the Borel cardinality of the isomorphism relation for nuclear simple separable C*-algebras: It is turbulent, yet Borel reducible to the action of the automorphism group of the Cuntz algebra O_2 on its closed subsets. The same bounds are obtained for affine homeomorphism of metrizable Choquet simplexes. As a by-product we recover a result of Kechris and Solecki, namely, that homeomorphism of compacta in the Hilbert cube is Borel reducible to a Polish group action. These results depend intimately on the classification theory of nuclear simple C*-algebras by K-theory and traces. Both of necessity and in order to lay the groundwork for further study on the Borel complexity of C*-algebras, we prove that many standard C*-algebra constructions and relations are Borel, and we prove Borel versions of Kirchberg's O_2-stability and embedding theorems. We also find a C*-algebraic witness for a K_σhard equivalence relation.
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