Decomposition rank of approximately subhomogeneous C*-algebras
Decomposition rank of approximately subhomogeneous C*-algebras
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DOI：
10.1515/forum-2020-0018
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发表时间：
2015-05
影响因子：
0.8
通讯作者：
G. Elliott;Z. Niu;Luis Santiago;A. Tikuisis
中科院分区：
文献类型：
--
作者：
G. Elliott;Z. Niu;Luis Santiago;A. Tikuisis
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.
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.