THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS

Abstract

Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasi-ordered group containing (G, G+). Let and be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from to . This paper studies the connection between Ker γGF, G+ and the minimal closed ideal of . It is proved that if G is amenable and GF≠ G+, then Ker γGF, G+ is exactly the minimal closed non-trivial ideal of . As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.