最小动力学与K理论刚性：Elliott猜想
Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture
摘要：
设X是有限覆盖维的无限紧可度量化空间，h是X的极小同胚.证明了C（X）与h的交叉积张量地吸收Jiang-Su代数，并且具有有限的核维数.因此，这些代数是由它们的分次有序K-理论在它们的投影分离迹的必要条件下决定的同构。这个结果特别适用于由唯一遍历同胚产生的交叉积。
英文摘要：
Let X be an infinite, compact, metrizable space of finite covering dimension and h a minimal homeomorphism of X. We prove that the crossed product of C(X) by h absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms.
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