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Title: The Primitive Ideal Space of Two-Step Nilpotent Group C*-Algebras
Authors: Baggett, L.
Packer, J. 
Issue Date: Sep-1994
Citation: Baggett, L., Packer, J. (1994-09). The Primitive Ideal Space of Two-Step Nilpotent Group C*-Algebras. Journal of Functional Analysis 124 (2) : 389-426. ScholarBank@NUS Repository.
Abstract: Let N be a two-step nilpotent, locally compact, second countable group having center Z and quotient A = N/Z. We study the Jacobson topology on the primitive ideal space Prim C*(N) of the group C*-algebra of N. We are able to describe this topology in terms of convergence of subgroup-representation pairs, as used by the first author in an earlier work. Under appropriate conditions on N, we are able to describe Prim C*(N) globally as the quotient of a principal  bundle over Ẑ modulo an equivalence relation determined entirely by the group structure. We use this second result to compute the primitive ideal spaces of several examples, including all finitely generated, non-torsion two-step nilpotent discrete groups of rank less than or equal to five. Applications of our methods to more general central twisted crossed products are discussed. © 1994 Academic Press. All rights reserved.
Source Title: Journal of Functional Analysis
ISSN: 00221236
DOI: 10.1006/jfan.1994.1112
Appears in Collections:Staff Publications

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