GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS

GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS

Let Γ be a totally ordered abelian group and I an order ideal in Γ. We prove a theorem which relates the structure of the Toeplitz algebra T(Γ) to the structure of the Toeplitz algebras T(I) and T(Γ/I). We then describe the primitive ideal space of the Toeplitz algebra T(Γ) when the set Σ(Γ) of orde...

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Veröffentlicht in:Glasgow mathematical journal 2007-01, Vol.49 (1), p.81-92
Hauptverfasser: ADJI, SRIWULAN, RAEBURN, IAIN, ROSJANUARDI, RIZKY
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46L55
Algebra
Mathematical problems
Theorems
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ROSJANUARDI, RIZKY
description Let Γ be a totally ordered abelian group and I an order ideal in Γ. We prove a theorem which relates the structure of the Toeplitz algebra T(Γ) to the structure of the Toeplitz algebras T(I) and T(Γ/I). We then describe the primitive ideal space of the Toeplitz algebra T(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 of T(Γ) when 0→ I→ Γ→ Γ/I→ 0 is a non-trivial group extension.
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subjects 46L55
Algebra
Mathematical problems
Theorems
title GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS
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