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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: wulan@cs.usm.my
IAIN RAEBURN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong NSW 2522, Australia e-mail: raeburn@uow.edu.au
RIZKY ROSJANUARDI
Affiliation:
Department of Mathematics, Universitas Pendidikan Indonesia, Jl. Dr. Setia Budhi 229, Bandung 40154, Indonesia e-mail: rizky@upi.edu
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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

REFERENCES

1.Adji, S., Invariant ideals of crossed products by semigroups of endomorphisms, in Functional analysis and global analysis (Sunada, T. and Sy, P. W., Eds.) (Springer-Verlag, 1997), 1–8.Google Scholar
2.Adji, S., Semigroup crossed products and the structure of Toeplitz algebras, J. Operator Theory 44 (2000), 139–150.Google Scholar
3.Adji, S., Laca, M., Nilsen, M. and Raeburn, I., Crossed products by semigroups of endomorphisms and the Toeplitz algebras of ordered groups, Proc. Amer. Math. Soc. 122 (1994), 1133–1141.CrossRefGoogle Scholar
4.Adji, S. and Raeburn, I., The ideal structure of Toeplitz algebras, Integral Equations and Operator Theory 48 (2004), 281–293.CrossRefGoogle Scholar
5.Adji, S., Raeburn, I. and Ströh, A., An index theorem for Toeplitz algebras on totally ordered groups, Proc. Amer. Math. Soc. 126 (1998), 2993–2998.CrossRefGoogle Scholar
6.Clifford, A. H., Note on Hahn's theorem on ordered groups, Proc. Amer. Math. Soc. 5 (1954), 860–863.Google Scholar
7.Coburn, L. A., The C*-algebra generated by an isometry I, Bull. Amer. Math. Soc. 13 (1967), 722–726.CrossRefGoogle Scholar
8.Douglas, R. G., On the C*-algebra of a one-parameter semigroup of isometries, Acta Math. 128 (1972), 143–152.CrossRefGoogle Scholar
9.Echterhoff, S., On induced covariant systems, Proc. Amer. Math. Soc. 108 (1990), 703–706.CrossRefGoogle Scholar
10.Laca, M. and Raeburn, I., Semigroup crossed products and the Toeplitz algebras of nonabelian groups, J. Functional Analysis 139 (1996), 415–440.CrossRefGoogle Scholar
11.Lorch, J. and Xu, Q., Quasi-lattice ordered groups and Toeplitz algebras, J. Operator Theory 50 (2003), 221–247.Google Scholar
12.Murphy, G. J., Ordered groups and Toeplitz algebras, J. Operator Theory 18 (1987), 303–326.Google Scholar
13.Nica, A., C*-algebras generated by isometries and Wiener-Hopf operators, J. Operator Theory 27 (1992), 17–52.Google Scholar
14.Raeburn, I. and Williams, D. P., Morita equivalence and continuous-trace C*-algebras, Math. Surveys and Monographs, Vol. 60 (Amer. Math. Soc., Providence, 1998).CrossRefGoogle Scholar