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GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS

Published online by Cambridge University Press:  01 January 2007

SRIWULAN ADJI ,
IAIN RAEBURN  and
RIZKY ROSJANUARDI
SRIWULAN ADJI
Affiliation:
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia e-mail: [email protected]
IAIN RAEBURN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong NSW 2522, Australia e-mail: [email protected]
RIZKY ROSJANUARDI
Affiliation:
Department of Mathematics, Universitas Pendidikan Indonesia, Jl. Dr. Setia Budhi 229, Bandung 40154, Indonesia e-mail: [email protected]
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Abstract.

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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.

Keywords

46L55
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 81 - 92
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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