Decomposition rank of approximately subhomogeneous C*-algebras
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AbstractIt is shown that every Jiang–Su stable approximately subhomogeneous {{\mathrm{C}^{*}}}-algebra has finite decomposition rank. This settles a key direction of the Toms–Winter conjecture for simple approximately subhomogeneous {{\mathrm{C}^{*}}}-algebras. A key step in the proof is that subhomogeneous {{\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 {{\mathrm{C}^{*}}}-algebras associated to minimal homeomorphisms with mean dimension zero.
2018 ◽
Vol 10
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pp. 447-469
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1989 ◽
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pp. 593-624
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pp. 229-238
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pp. 1080-1098
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pp. 531-533
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1993 ◽
Vol 04
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pp. 289-317
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