Decomposition rank of UHF-absorbing c* -algebras
Decomposition rank of UHF-absorbing c* -algebras
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DOI：
10.1215/00127094-2826908
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发表时间：
2013-03
影响因子：
2.5
通讯作者：
H. Matui;Yasuhiko Sato
中科院分区：
文献类型：
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作者：
H. Matui;Yasuhiko Sato
设A是一个有唯一迹态的可分单C*-代数.证明了若A是核拟对角的，则A在泛UHF-代数张量下的分解秩至多为1。然后证明了A是核的、拟对角的和有严格比较的当且仅当A有有限分解秩。对于这样的A，我们也给出了一个直接的证明，证明了张量为UHF-代数的A的迹秩为零。应用这一特征，我们得到了一个反例的Powers-Sakai猜想。
Let A be a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHF-algebra has decomposition rank at most one. Then it is proved that A is nuclear, quasidiagonal and has strict comparison if and only if A has finite decomposition rank. For such A, we also give a direct proof that A tensored with a UHF-algebra has tracial rank zero. Applying this characterization, we obtain a counter-example to the Powers-Sakai conjecture.