Deformation Retraction of Groups and Toeplitz Algebras

群的形变收缩及Toeplitz代数(英文)

Let （G, G＋） be a quasi-partial ordered group such that G＋^0=G＋∩G＋^-1 is a non-trivial subgroup of G. Let [G] be the collection of left cosets and [G＋] be its positive. Denote by T^G＋ and T^[G＋] the associated Toeplitz algebras. We prove that T^G＋ is unitarily isomorphic to a C^＊-subalgebra of T^｜G＋｜⊙（G＋^＋） if there exists a deformation retraction from G onto G＋^0. Suppose further that G＋^0 is normal, then ,T^G＋ and ,T^｜G＋｜⊙GT^＊（G＋^0） are unitarily equivalent.

设G为一个离散群,(G,G_+)为一个拟偏序群使得G_+~0=G_+∩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T^(G_+)和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T^(G_+)酉同构于T^([G_+])×C_r~*(G_+~0)的一个C_-~*c子代数。若进一步,G_+~0还为G的一个正规子群,则T^(G_+)与T^([G_+])×C_r~*(G_+~0)酉同构。