GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS
Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 81-92
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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.
ADJI, SRIWULAN; RAEBURN, IAIN; ROSJANUARDI, RIZKY. GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS. Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 81-92. doi: 10.1017/S0017089507003436
@article{10_1017_S0017089507003436,
author = {ADJI, SRIWULAN and RAEBURN, IAIN and ROSJANUARDI, RIZKY},
title = {GROUP {EXTENSIONS} {AND} {THE} {PRIMITIVE} {IDEAL} {SPACES} {OF} {TOEPLITZ} {ALGEBRAS}},
journal = {Glasgow mathematical journal},
pages = {81--92},
year = {2007},
volume = {49},
number = {1},
doi = {10.1017/S0017089507003436},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003436/}
}
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%0 Journal Article %A ADJI, SRIWULAN %A RAEBURN, IAIN %A ROSJANUARDI, RIZKY %T GROUP EXTENSIONS AND THE PRIMITIVE IDEAL SPACES OF TOEPLITZ ALGEBRAS %J Glasgow mathematical journal %D 2007 %P 81-92 %V 49 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003436/ %R 10.1017/S0017089507003436 %F 10_1017_S0017089507003436
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