THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS
Xuqingxiang · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2000
Let G be a discrete group and (G,G+)an ordered group.Let(G,GF) be the minimal quasiordered group containing (G,G+).Let TG+(G) and TGF(G) be the corresponding Toeplitz algebras,and γGF,G+ the natural C-algebra morphism from TG+(G) to TGF(G).This paper studies the connection between KerγGF,G+ and the minimal closed ideal of TG+(G).It is proved that if G is amenable and GF≠G+,then ker γGF,G+ is exactly the minimal closed non-trivial ideal of TG+(G).As an application,in the last part of this paper,a character of K-groups of Toeplitz algebras on ordered groups is clarified.