TOEPLITZ ALGEBRAS AND INFINITE SIMPLE C*-ALGEBRAS ASSOCIATED WITH REDUCED GROUP C*-ALGEBRAS

摘要

Assume that F is the free product of an arbitrary number of finite cyclic groups and any free group, and the generators of F are ,sfi,g2,.... Let F+ consist of the unit e of F and all those re-duced words of the form g~1'g/jr ...#￡* where n,ti2,..,,nk are positive integers, and let R+ be the projection onto the subspace /2(T+) of I2(F). We prove that the C*-algebra C"(F, R+) generated by the reduced group C*-algebra Cr*F and R+ has either one or two non-trivial closed ideals which are stable and of real rank zero. This construction results some purely infinite simple C*-algebras.