Unitary groups and augmented Cuntz semigroups of separable simple Z-Stable C*-algebras

作者：Lin, Huaxin^*

来源：International Journal of Mathematics, 2022, 33(02): 2250018.

DOI：10.1142/S0129167X22500185

• Simple C*
• algebras
• Cuntz semigroups

Let A be a separable simple exact Z-stable C*-algebra. We show that the unitary group of A has the cancellation property. If A has continuous scale then the Cuntz semigroup of (A) over tilde has strict comparison property and a weak cancellation property. Let C be a 1-dimensional noncommutative CW complex with K-1(C) = {0}. Suppose that lambda : Cu-similar to(C) -> Cu-similar to(A) is a morphism in the augmented Cuntz semigroups which is strictly positive. Then there exists a sequence of homomorphisms phi(n) : C -> A such that lim(n ->infinity)Cu(similar to)(phi(n)) = lambda. This result leads to the proof that every separable amenable simple C*-algebrain the UCT class has rationally generalized tracial rank at most one.