Abstract It is shown that every Jiang–Su stable approximately subhomogeneous C * {{\mathrm{C}^{*}}} -algebra has finite decomposition rank. This settles a key direction of the Toms–Winter conjecture for simple approximately subhomogeneous C * {{\mathrm{C}^{*}}} -algebras. A key step in the proof is that subhomogeneous C * {{\mathrm{C}^{*}}} -algebras are locally approximated by a certain class of more tractable subhomogeneous algebras, namely a non-commutative generalization of the class of cell complexes. The result is applied, in combination with other recent results, to show classifiability of crossed product C * {{\mathrm{C}^{*}}} -algebras associated to minimal homeomorphisms with mean dimension zero.

中文翻译：

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近似次齐次 C*-代数的分解秩

摘要 证明了每一个江苏稳定的近似次齐次C * {{\mathrm{C}^{*}}} -代数都具有有限的分解秩。这为简单的近似次齐次 C * {{\mathrm{C}^{*}}} -代数确定了 Toms-Winter 猜想的一个关键方向。证明中的一个关键步骤是次齐次 C * {{\mathrm{C}^{*}}} -代数被某一类更易处理的次齐次代数局部逼近，即细胞类的非交换泛化复合体。该结果与其他最近的结果相结合，用于显示与平均维数为零的最小同胚相关的交叉积 C * {{\mathrm{C}^{*}}} -代数的可分类性。