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arXiv 1406.0883math.OA
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高维Z-稳定AH代数

High-dimensional Z-stable AH algebras

Aaron Tikuisis

摘要:

证明了C(X,U)形式的C*-代数不是拓扑维数小于X的次齐次C* 代数的归纳极限,其中U是UHF代数.这是在鲜明的对比降维现象(i)简单的归纳极限,这样的代数,其中分类意味着低维近似,(ii)当维度测量使用分解秩,作为作者和温特证明,博士(C(X,U))$\leq$ 2。

英文摘要:

It is shown that a C*-algebra of the form C(X,U), where U is a UHF algebra, is not an inductive limit of subhomogeneous C*-algebras of topological dimension less than that of X. This is in sharp contrast to dimension-reduction phenomenon in (i) simple inductive limits of such algebras, where classification implies low-dimensional approximations, and (ii) when dimension is measured using decomposition rank, as the author and Winter proved that dr(C(X,U)) $\leq$ 2.

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。

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