Abstract
Our aim in this paper is to describe the construction of Cuntz-Pimsner C*-algebras and a class of distinguished, nonselfadjoint, subal-gebras of these C*-algebras, called tensor algebras. We shall discuss the representations of these algebras and present some results and examples. In section 1 we present sufficient conditions for the simplicity of Cuntz-Pimsner algebras and in section 2 we discuss dilations and extensions of representations of the tensor algebras leading to the identification of their C*-envelopes. Most of the results (with proofs) can be found in the work of Pimsner [26] and in a joint work with P. Muhly [21] and [22]
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Solel, B. (1997). Operator Algebras Over C*-Correspondences. In: Katavolos, A. (eds) Operator Algebras and Applications. NATO ASI Series, vol 495. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5500-7_14
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DOI: https://doi.org/10.1007/978-94-011-5500-7_14
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