$K_1$中一类带挠的单$C^*$ -代数的分类
Classification of certain simple $C^*$-algebras with torsion in $K_1$
摘要：
我们证明了Elliott不变量是一类$C^*$ -代数的分类不变量，这些代数是$$ \{f\in C(\T)\otimes M_n: f(x_i)\in M_{d_i}, i=1,2,...,N\}, $$形式的积木块的有限直和序列的简单单位无穷维归纳极限，其中$x_1,x_2,...,x_N\in\T$，$d_1,d_2,...,d_N$是整除$n$的整数，并且$M_{d_i}$被酉嵌入到$M_n$中.此外，我们证明了存在性和唯一性定理的 *-同态之间的代数，我们确定的范围内的不变量。
英文摘要：
We show that the Elliott invariant is a classifying invariant for the class of $C^*$-algebras that are simple unital infinite dimensional inductive limits of sequences of finite direct sums of building blocks of the form $$ \{f\in C(\T)\otimes M_n: f(x_i)\in M_{d_i}, i=1,2,...,N\}, $$ where $x_1,x_2,...,x_N\in\T$, $d_1,d_2,...,d_N$ are integers dividing $n$, and $M_{d_i}$ is embedded unitally into $M_n$. Furthermore we prove existence and uniqueness theorems for *-homomorphisms between such algebras and we identify the range of the invariant.
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