论文标题
$ \ mathrm {c}^*$ - 与同构相关的代数，由矢量束扭曲而不是有限维空间
$\mathrm{C}^*$-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces
论文作者
论文摘要
在本文中，我们研究了与$ \ mathrm {c}^*$相关的cuntz-pimsner代数 - 从$ \ mathrm {c}^^$ algebra Clansification的角度来看，交换$ \ mathrm {c}^*$ - 代数。我们表明，当对应关系来自一个有限的无限无限的紧凑型公制空间的同态同态时，由矢量束扭曲时，由此产生的cuntz--pimsner代数具有有限的核维度。当同态性最小化时，这需要对这些$ \ mathrm {c}^*$ - Elliott不变的代数进行分类。这建立了二分法：当矢量束的排名占1时，cuntz--pimsner代数的排名稳定。否则，它纯粹是无限的。 对于一个cuntz- pimsner代数，即无限紧凑的公制空间的最小同态形态，$ x $ twest twest twess twill line bundle twews twess of $ x $，我们介绍了轨道破坏性的亚代词。没有关于$ x $的尺寸的假设，我们表明它们是中央大的亚代词，因此简单而稳定。当$ x $的尺寸是有限的时，它们是$ \ Mathcal {z} $ - 稳定的，因此由Elliott不变性分类。
In this paper we study Cuntz--Pimsner algebras associated to $\mathrm{C}^*$-correspondences over commutative $\mathrm{C}^*$-algebras from the point of view of the $\mathrm{C}^*$-algebra classification programme. We show that when the correspondence comes from an aperiodic homeomorphism of a finite-dimensional infinite compact metric space $X$ twisted by a vector bundle, the resulting Cuntz--Pimsner algebras have finite nuclear dimension. When the homeomorphism is minimal, this entails classification of these $\mathrm{C}^*$-algebras by the Elliott invariant. This establishes a dichotomy: when the vector bundle has rank one, the Cuntz--Pimsner algebra has stable rank one. Otherwise, it is purely infinite. For a Cuntz--Pimsner algebra of a minimal homeomorphism of an infinite compact metric space $X$ twisted by a line bundle over $X$, we introduce orbit-breaking subalgebras. With no assumptions on the dimension of $X$, we show that they are centrally large subalgebras and hence simple and stably finite. When the dimension of $X$ is finite, they are furthermore $\mathcal{Z}$-stable and hence classified by the Elliott invariant.
