Hausdorffified algebraic K1-groups and invariants for C∗-algebras with the ideal property
Hausdorffified algebraic K1-groups and invariants for C∗-algebras with the ideal property
复制标题
具有理想性质的 Hausdorffified 代数 K1 群和 C-代数的不变量
DOI：
10.2140/akt.2020.5.43
复制
发表时间：
2019-05
影响因子：
0.6
通讯作者：
Li Liangqing
中科院分区：
文献类型：
--
作者：
Gong guihua;Jiang Chunlan;Li Liangqing
A $C^*$-algebra $A$ is said to have the ideal property if each closed two-sided ideal of $A$ is generated by the projections inside the ideal, as a closed two sided ideal. $C^*$-algebras with the ideal property are generalization and unification of real rank zero $C^*$-algebras and unital simple $C^*$-algebras. It is long to be expected that an invariant (see [Stev] and [Ji-Jiang], [Jiang-Wang] and [Jiang1]) , we call it $Inv^0(A)$ (see the introduction), consisting of scaled ordered total $K$-group $(\underline{K}(A), \underline{K}(A)^{+},\Sigma A)_{\Lambda}$ (used in the real rank zero case), the tracial state space $T(pAp)$ of cutting down algebra $pAp$ as part of Elliott invariant of $pAp$ (for each $[p]\in\Sigma A$) with a certain compatibility, is the complete invariant for certain well behaved class of $C^*$-algebras with the ideal property (e.g., $AH$ algebras with no dimension growth). In this paper, we will construct two non isomorphic $A\mathbb{T}$ algebras $A$ and $B$ with the ideal property such that $Inv^0(A)\cong Inv^0(B)$. The invariant to differentiate the two algebras is the Hausdorffifized algebraic $K_1$-groups $U(pAp)/\overline{DU(pAp)}$ (for each $[p]\in\Sigma A$) with a certain compatibility condition. It will be proved in [GJL] that, adding this new ingredients, the invariant will become the complete invariant for $AH$ algebras (of no dimension growth) with the ideal property.
登录
查看更多内容
DOI：
10.1090/s0002-9947-00-02680-5
发表时间：
2000-09
影响因子：
1.3
作者：
Huaxin Lin
通讯作者：
Huaxin Lin
AH 代数的同态
影响因子：
0.8
作者：
Lin Huaxin
通讯作者：
Lin Huaxin
影响因子：
--
作者：
B. Blackadar;A. Kumjian;M. Rørdam
通讯作者：
B. Blackadar;A. Kumjian;M. Rørdam
DOI：
10.24033/msmf.385
发表时间：
1997
期刊：
--
影响因子：
--
作者：
K. Thomsen
通讯作者：
K. Thomsen
影响因子：
--
作者：
M. Dadarlat
通讯作者：
M. Dadarlat