GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS

Abstract

Abstract.Let Γ be a totally ordered abelian group andIan order ideal in Γ. We prove a theorem which relates the structure of the Toeplitz algebraT(Γ) to the structure of the Toeplitz algebrasT(I) andT(Γ/I). We then describe the primitive ideal space of the Toeplitz algebraT(Γ) when the set Σ(Γ) of order ideals in Γ is well-ordered, and use this together with our structure theorem to deduce information about the ideal structure ofT(Γ) when 0→I→ Γ→ Γ/I→ 0 is a non-trivial group extension.