arXiv 1702.010732017-02math.OA

关于单非幺正顺从C* 代数的分类，II

On classification of simple non-unital amenable C*-algebras, II

Guihua Gong, Huaxin Lin

备注：: a homotopy lemma and an appendix are added. Revision of Feb. 2020

摘要：

给出了广义迹秩为1的顺从简单稳定无投影C* 代数-代数的一个分类定理，其$K_0$在满足泛系数定理的迹上为零.其中一个表示为具有唯一迹态的${\cal Z}_0$，另一个表示为$K_0({\cal Z}_0)=\mathbb{Z}$和$K_1({\cal Z}_0)=\{0\}.$。设$A$和$B$是两个满足UCT的可分单$C^*$ -代数，具有有限的核维数。我们证明了$A\otimes {\cal Z}_0\cong B\otimes {\cal Z}_0$当且仅当${\rm Ell}(B\otimes {\cal Z}_0)={\rm Ell}(B\otimes {\cal Z}_0).$一类简单可分的$C^*$ -代数是近似次齐次的，其具有有界维数的谱被证明为耗尽了形式为$A\otimes {\cal Z}_0,$的$C^*$ -代数的所有可能的Elliott不变量，其中$A$是任何有限可分的简单顺从的$C^*$ -代数。设$A$和$B$是两个有限可分的单$C^*$ -代数，它们具有满足UCT的有限核维数，使得迹在$K_0(A)$和$K_0(B)$（但是任意的$K_1$）上消失.在这种情况下的主要结果的一个结果是，$A\cong B$当且仅当$A$和$B$具有同构的艾略特不变量。

英文摘要：

We present a classification theorem for amenable simple stably projectionless C*-algebras with generalized tracial rank one whose $K_0$ vanish on traces which satisfy the Universal Coefficient Theorem. One of them is denoted by ${\cal Z}_0$ which has a unique tracial state and $K_0({\cal Z}_0)=\mathbb{Z}$ and $K_1({\cal Z}_0)=\{0\}.$ Let $A$ and $B$ be two separable simple $C^*$-algebras satisfying the UCT and have finite nuclear dimension. We show that $A\otimes {\cal Z}_0\cong B\otimes {\cal Z}_0$ if and only if ${\rm Ell}(B\otimes {\cal Z}_0)={\rm Ell}(B\otimes {\cal Z}_0).$ A class of simple separable $C^*$-algebras which are approximately sub-homogeneous whose spectra having bounded dimension is shown to exhaust all possible Elliott invariant for $C^*$-algebras of the form $A\otimes {\cal Z}_0,$ where $A$ is any finite separable simple amenable $C^*$-algebras. Suppose that $A$ and $B$ are two finite separable simple $C^*$-algebras with finite nuclear dimension satisfying the UCT such that traces vanishe on $K_0(A)$ and $K_0(B)$ (but arbitrary $K_1$). One consequence of the main results in this situation is that $A\cong B$ if and only if $A$ and $B$ have the isomorphic Elliott invariant.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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