Unitary groups and augmented Cuntz semigroups of separable simple Z-Stable C∗-algebras
Unitary groups and augmented Cuntz semigroups of separable simple Z-Stable C∗-algebras
复制标题
可分离简单 Z 稳定 C 代数的酉群和增广 Cuntz 半群
DOI：
10.1142/s0129167x22500185
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发表时间：
2022
影响因子：
0.6
通讯作者：
Lin, Huaxin
中科院分区：
文献类型：
--
作者：
Lin, Huaxin
让be是一个可分离的简单精确稳定代数。我们证明酉群 具有取消性质。如果具有连续尺度，则 Cuntz 半群具有严格比较性和弱取消性。设 为一维非交换 CW 复形，假设 是增广 Cuntz 半群中的态射，且严格为正。那么存在一系列同态，使得这个结果证明了 UCT 类的每个可分离的简单代数都具有至多 1 的有理概括的踪迹等级。
Letbe a separable simple exact-stable-algebra. We show that the unitary group ofhas the cancellation property. Ifhas continuous scale then the Cuntz semigroup ofhas strict comparison property and a weak cancellation property. Letbe a 1-dimensional noncommutative CW complex withSuppose thatis a morphism in the augmented Cuntz semigroups which is strictly positive. Then there exists a sequence of homomorphismssuch thatThis result leads to the proof that every separable amenable simple-algebrain the UCT class has rationally generalized tracial rank at most one.