康托尔集与奇维球面乘积的极小动力系统的C* 代数
C*-algebras of minimal dynamical systems of the product of a Cantor set and an odd dimensional sphere
摘要：
设β：S^\to S^n，其中n = 2k + 1，k \geq 1，是奇维球面的非唯一遍历极小自同态的已知例子之一.对于每一个这样的极小动力系统（S^n，β），存在一个Cantor极小系统（X，α），使得相应的乘积系统（X x S^n，αx β）是极小的，并且由此得到的交叉积C*-代数C（X x S^n）\rtimes_{αx β} \mathbb{Z}是迹逼近区间代数（TAI）.这就需要对这样的C* 代数进行分类。此外，极小Cantor系统（X，α）使得C（X x S^n）\rtimes_β \mathbb{Z}上的每个迹态诱导K_0-群上的相同态，并且使得C（S^n）\rtimes_β \mathbb{Z}嵌入C（X x S^n）\rtimes_{αx β} \mathbb{Z}保持迹态空间.这意味着C（S^n）\rtimes_β \mathbb{Z}在用泛UHF代数张量后是TAI，这反过来表明这些奇维球面的极小同态的例子的C* 代数-代数是由它们的迹状态空间分类的。
英文摘要：
Let β: S^n \to S^n, for n = 2k + 1, k \geq 1, be one of the known examples of a non-uniquely ergodic minimal diffeomorphism of an odd dimensional sphere. For every such minimal dynamical system (S^n, β) there is a Cantor minimal system (X, α) such that the corresponding product system (X x S^n, αx β) is minimal and the resulting crossed product C*-algebra C(X x S^n) \rtimes_{αx β} \mathbb{Z} is tracially approximately an interval algebra (TAI). This entails classification for such C*-algebras. Moreover, the minimal Cantor system (X, α) is such that each tracial state on C(X x S^n) \rtimes_β \mathbb{Z} induces the same state on the K_0-group and such that the embedding of C(S^n) \rtimes_β \mathbb{Z} into C(X x S^n) \rtimes_{αx β} \mathbb{Z} preserves the tracial state space. This implies C(S^n) \rtimes_β \mathbb{Z} is TAI after tensoring with the universal UHF algebra, which in turn shows that the C*-algebras of these examples of minimal diffeomorphisms of odd dimensional spheres are classified by their tracial state spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
