Representations of Cuntz-Pimsner Algebras

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