Fowler, Neal J.; Muhly, Paul S.; and Raeburn, Iain, 2003, Representations of Cuntz-Pimsner Algebras, Indiana University Mathematics Journal, 52(3), 569-605.
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 I (I) in Ox induced by appropriately invariant ideals I in A, and identify the quotients Ox/I(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.