| 许庆祥.群的形变收缩及Toeplitz代数[J].数学研究及应用,2006,26(1):9~13 |
| 群的形变收缩及Toeplitz代数 |
| Deformation Retraction of Groups and Toeplitz Algebras |
| 投稿时间：2004-02-23 |
| DOI：10.3770/j.issn:1000-341X.2006.01.002 |
| 中文关键词: Toeplitz代数 拟偏序群. |
| 英文关键词:Toeplitz algebra quasi-partial ordered group. |
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| 摘要点击次数: 2487 |
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| 中文摘要: |
| 设$G$为一个离散群, $(G,G_+)$为一个拟偏序群使得$G^0_+=G_+\cap G^{-1}_+$为$G$的非平凡子群.令$[G]$为$G$关于$G^0_+$的左倍集全体, $|G_+|$为$[G]$的正部.记${\cal T}^{G_+}$和${\cal T}^{[G_+]}$为相应的Toeplitz代数.当存在一个从$G$到$G^0_+$上的形变收缩映照时,我们证明了${\cal T}^{G_+}$酉同构于${\cal T}^{[G_+]}\otimes C^*_r(G^0_+)$的一个$C^*$-子代数.若进一步, $G^0_+$还为$G$的一个正规子群,则${\cal T}^{G_+}$与${\cal T}^{[G_+]}\otimes C^*_r(G^0_+)$酉同构. |
| 英文摘要: |
| Let $(G,G_+)$ be a quasi-partial ordered group such that $G_+^0=G_+\cap G_+^{-1}$ is a non-trivial subgroup of $G$. Let $[G]$ be the collection of left cosets and $[G_+]$ be its positive. Denote by ${\cal T}^{G_+}$ and ${\cal T}^{[G_+]}$ the associated Toeplitz algebras. We prove that ${\cal T}^{G_+}$ is unitarily isomorphic to a $C^*$-subalgebra of ${\cal T}^{[G_+]}\otimes C_r^*(G_+^0)$ if there exists a deformation retraction from $G$ onto $G_+^0$. Suppose further that $G_+^0$ is normal, then ${\cal T}^{G_+}$ and ${\cal T}^{[G_+]}\otimes C_r^*(G_+^0)$ are unitarily equivalent. |
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