Journal of Operator Theory

Volume 34, Issue 1, Summer 1995 pp. 91-124.

Twisted group C*-algebras for two-step nilpotent and generalized discrete Heisenberg groups

Authors: Soo Teck Lee (1) and Judith A. Packer (2)
Author institution:(1) Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511, Republic of Singapore
(2) Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511, Republic of Singapore

Summary: Twisted group C*-algebras associated to two-step nilpotent groups are studied and their primitive ideal spaces are described as fibre bundles over an abelian group with fibre spaces being quasi-orbit spaces for affine group actions. Under appropriate conditions a *-isomorphism is constructed between such a C*-algebra and the C*-algebra of continuous sections of a C*-bundle over an abelian group with fibres stably isomorphic to twisted abelian group C*-algebras, thus simplifying the description of the corresponding primitive ideal spaces. These results are then applied to the study of twisted group C*-algebras associated to generalized discrete Heisenberg groups. The multiplier groups are computed, and a setwise parametrization of the primitive ideal spaces is given. For discrete Heisenberg groups of rank greater than or equal to five it is shown that the associated twisted group C*-algebras can always be decomposed as C*-algebras of sections of C*-bundles over a torus with fibres being matrix algebras over non-commutative tori.

Keywords: Locally compact group, C*-algebra, primitive ideal space.

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