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Let X be a Hilbert bimodule over a C * -algebra A. We analyse the structure of the associated Cuntz-Pimsner algebra X and related algebras using representation-theoretic methods. In particular, we study the ideals (I) in X induced by appropriately invariant ideals I in A, and identify the quotients X/(I) as relative Cuntz-Pimsner algebras of Muhly and Solel. We also prove a gauge-invariant uniqueness theorem for X, and investigate the relationship between X and an alternative model proposed by Doplicher, Pinzari and Zuccante.
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Fowler et al. (2003) studied this question.
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