论文标题
可分离的简单Z稳定C* - 代数的统一组和增强的Cuntz Semigroups
Unitary groups and augmented Cuntz semigroups of separable simple Z-stable C*-algebras
论文作者
论文摘要
令$ a $为可分离的简单精确$ {\ cal z} $ - 稳定$ c^*$ - 代数。我们表明，$ {\ tilde a} $的unitay组具有取消属性。如果$ a $具有连续规模，则$ \ tilde a $的Cuntz Semigroup具有严格的比较属性和弱取消属性。让$ c $为1维的非惯用CW复合体，$ k_1（c）= \ {0 \}。然后，存在一系列同构$ ϕ_n：c \ to a $，以至于$ \ lim_ {n \ to \ fo \ infty} {\ rm cu}^\ sim（ϕ_n）=λ。$。$这会导致每个可分开的简单的简单的简单的$ c^*$ - alge-alge-algebra intation intation intation intation intation in the the uct in the uct in the uct in the the uct in the uct in the uct in rcation in ractial in ractial incation in ractial incation。
Let $A$ be a separable simple exact ${\cal Z}$-stable $C^*$-algebra. We show that the unitay group of ${\tilde A}$ has the cancellation property. If $A$ has continuous scale, the Cuntz semigroup of $\tilde A$ has the strict comparison property and a weak cancellation property. Let $C$ be a 1-dimensional non-commutative CW complex with $K_1(C)=\{0\}.$ Suppose that $λ: {\rm Cu}^\sim(C)\to {\rm Cu}^\sim(A)$ is a morphism in Cuntz semigroups which is strictly positive. Then there exists a sequence of homomorphisms $ϕ_n: C\to A$ such that $\lim_{n\to\infty}{\rm Cu}^\sim(ϕ_n)=λ.$ This result leads to the proof that every separable amenable simple $C^*$-algebra in the UCT class has rationally generalized tracial rank at most one.
