| Deformation Retraction of Groups and Toeplitz Algebras |
| Received:February 23, 2004 |
| Key Words:
Toeplitz algebra quasi-partial ordered group.
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| Fund Project:the National Natural Foundation of China (10371051), Shanghai Natural Science Foundation (05ZR14094) and Shanghai Municipal Education Commission (05DZ04) |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2006.01.002 |
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