We show that two separable stably projectionless simple C*-algebras A and B with $gTR(A) \le 1$ and $gTR(B) \le 1$ which satisfy the UCT are isomorphic if and only if they have the isomorphic Elliott invariant. A description of Elliott invariant is given. We show all possible simple scaled Elliott invariants can be reached by C*-algebras in the class. We show that these results imply that two separable simple C*-algebras with stable rank one and finite nuclear dimension which satisfy the UCT are isomorphic if and only if they have the same Elliott invariant.

中文翻译：

---

关于非单位服从简单 C*-代数的分类，II

我们证明了满足 UCT 的两个可分离稳定无投影简单 C*-代数 A 和 B 与 $gTR(A) \le 1$ 和 $gTR(B) \le 1$ 是同构的当且仅当它们具有同构 Elliott不变的。给出了艾略特不变量的描述。我们展示了所有可能的简单缩放 Elliott 不变量都可以通过类中的 C*-代数达到。我们表明，这些结果意味着两个可分离的简单 C*-代数具有稳定的 1 阶和有限核维数且满足 UCT 是同构的，当且仅当它们具有相同的 Elliott 不变量。