Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra m...Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (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 G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.展开更多
基金the National Natural Science Foundation of China!(No. 19901019) the YouthScience Foundation of Colleges and Universities o
文摘Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (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 G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.
