群的形变收缩及Toeplitz代数

摘要

设G为一个离散群,(G,G+)为一个拟偏序群使得G0+=G+∩G0-1为G的非平凡子群.令[G]为G关于G0+的左倍集全体,|G+|为|G|的正部.记TG+和T[G+]为相应的Toeplitz代数.当存在一个从G到G0+上的形变收缩映照时,我们证明了TG+酉同构于T[G+]( ) Cr*(G0+)的一个C*-子代数.若进一步,G0+还为G的一个正规子群,则TG+与T[G+]( )Cr*(G0+)酉同构.%Let (G, G+) be a quasi-partial ordered group such that G0+ = 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 TG+ and T[G+] the associated Toeplitz algebras. We prove that TG+ is unitarily isomorphic to a C*-subalgebra of T[G+]( ) Cr* (G0+) if there exists a deformation retraction from G onto G0+. Suppose further that G0+ is normal, then TG+ and T[G+] ( )Cr*(G0+) are unitarily equivalent.