Vol. 230, No. 1, 2007

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ISSN: 0030-8730
Ideal structure of C-algebras associated with C-correspondences

Takeshi Katsura

Vol. 230 (2007), No. 1, 107–145
Abstract

We study the ideal structure of C-algebras arising from C-correspondences. We prove that gauge-invariant ideals of our C-algebras are parameterized by certain pairs of ideals of original C-algebras. We show that our C-algebras have a nice property that should be possessed by a generalization of crossed products. Applications to crossed products by Hilbert C-bimodules and relative Cuntz–Pimsner algebras are also discussed.

Keywords
C-algebra, C-correspondence, Hilbert module, Cuntz–Pimsner algebras, ideal structure, crossed products
Mathematical Subject Classification 2000
Primary: 46L05, 46L55
Milestones
Received: 25 October 2003
Accepted: 8 December 2006
Published: 1 March 2007
Authors
Takeshi Katsura
Department of Mathematics
Hokkaido University
Kita 10, Nishi 8
Kita-Ku, Sapporo, 060-0810
Japan