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The structure of certain group C*-algebras

Published online by Cambridge University Press:  17 April 2009

Milan Pahor
Milan Pahor
Affiliation:
Department of Mathematics, The University of New South Wales, Kensington NSW 2033, Australia
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Abstract

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Let G be a separable locally compact group which admits a non-trivial compact normal subgroup. It is shown that the group C*-algebra C*(G) of G may be decomposed as a direct sum of ideals whose structure is determined up to *-isomorphism. Applications are given to Type 1, [FD]− groups; in particular it is shown that the group C*-algebra of such a group is a direct sum of homogeneous C*-algebras.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 169 - 174
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Baggett, L. and Kleppner, A., ‘Multiplier representations of abelian groups’, J. Funct. Anal. 14 (1973), 299–324.CrossRefGoogle Scholar
[2]Baggett, L. and Sund, T., ‘The Hausdorff dual problem for connected groups’, J. Funct. Anal. 43 (1981), 60–68.CrossRefGoogle Scholar
[3]Dixmier, J., C*-algebras (North-Holland, Amsterdam, 1977).Google Scholar
[4]Green, P., ‘The local structure of twisted covariance algebras’, Acta Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[6]Green, P., ‘The structure of imprimitivity algebras’, J. Funct. Anal. 36 (1980), 88–104.CrossRefGoogle Scholar
[6]Liukkonen, J.R., ‘Dual spaces of groups with pre-compact conjugacy classes’, Trans. Amer. Math. Soc. 180 (1973), 85–108.CrossRefGoogle Scholar
[7]Mackay, G.W., ‘Borel structures in groups and their duals’, Trans. Amer. Math. Soc. 85 (1957), 134–165.CrossRefGoogle Scholar
[8]Mackay, G.W., ‘Unitary representations of group extensions I’, Acta Math. 99 (1958), 265–311.CrossRefGoogle Scholar
[9]Palmer, T.W., ‘Classes of nonabelian, noncompact locally compact groups’, Rocky Mountain J. Math. 8 (1978), 683–741.CrossRefGoogle Scholar
[10]Pedersen, G., C*-algebras and their automorphism groups (Academic Press, 1979).Google Scholar
[11]Raeburn, I., ‘On group C*-algebras of bounded representation dimension’, Trans. Amer. Math. Soc. 272 (1982), 629–644.Google Scholar