Ideal structure of C^*-algebras associated with C^*-correspondences

2003/09/18 by Takeshi Katsura, Katsura, Takeshi · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Spectral Theory in Mathematical Physics #math.OA #msc:46L05 #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0309294

34 pages

arxiv created 2003/10/02 · arxiv updated 2009/12/01

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 which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C^*-bimodules and relative Cuntz-Pimsner algebras are also discussed.

Cited by

• Adding tails to C*-correspondences
• On morphisms of topological quivers
• Cuntz--Pimsner algebras of partial automorphisms twisted by vector bundles II: Nuclear dimension

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