On the classification of simple amenable $\mathrm{C}^{}$-algebras with finite decomposition rank, II
We prove that every unital simple separable \mathrm{C}^{*} -algebra A with finite decomposition rank which satisfies the UCT has the property that A\otimes Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott.
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| Published in: | Journal of noncommutative geometry Vol. 19; no. 1; pp. 73 - 104 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
14.06.2024
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| ISSN: | 1661-6952, 1661-6960 |
| Online Access: | Get full text |
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| Summary: | We prove that every unital simple separable \mathrm{C}^{*} -algebra A with finite decomposition rank which satisfies the UCT has the property that A\otimes Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott. |
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| ISSN: | 1661-6952 1661-6960 |
| DOI: | 10.4171/jncg/560 |