|
|
| |
| THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS |
| |
Citation： |
XU Qingxiang.THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS[J].Chinese Annals of Mathematics B,2000,21(3):367~374 |
| Page view： 1078
Net amount： 745 |
Authors： |
XU Qingxiang; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No. 19901019) and the Youth Science Foundation of Colleges and Universities of Shanghai, China (No.98QN75). |
|
|
| Abstract： |
Let $G$ be a discrete group and $(G,G_+)$ an ordered group. Let $(G, G_F)$ be the minimal quasi-ordered group containing $(G, G_+).$ Let $\Cal T^{G_+}(G)$ and $\Cal T^{G_F}(G)$ be the corresponding Toeplitz algebras, and $\ga^{G_F,G_+}$ the natural $C^*$-algebra morphism from $\Cal T^{G_+}(G)$ to $\Cal T^{G_F}(G)$. This paper studies the connection between Ker\,$\ga^{G_F,G_+}$ and the minimal closed ideal of $\Cal T^{G_+}(G)$. It is proved that if $G$ is amenable and $G_F\not=G_+,$ then Ker\,$\ga^{G_F,G_+}$ is exactly the minimal closed non-trivial ideal of $\Cal T^{G_+}(G)$. As an application, in the last part of this paper, a character of $K$-groups of Toeplitz algebras on ordered groups is clarified. |
Keywords： |
Discrete group, Toeplitz algebra, Minimal ideal |
Classification： |
47B35 |
|
|
Download PDF Full-Text
|
|
|
|
