Cuntz-Pimsner algebras for subproduct systems

Details Cuntz-Pimsner algebras for subproduct systems Cuntz-Pimsner algebras for subproduct systems

2011-07-14

arxiv.org/abs/1107.2812v1

Mathematics

Operator Algebras

33 pages

Scientific paper

In this paper we generalize the notion of Cuntz-Pimsner algebras of $C^*$-correspondences to the setting of subproduct systems. The construction is justified in several ways, including the Morita equivalence of the operator algebras under suitable conditions, and examples are provided to illustrate its naturality. We also demonstrate why some features of the Cuntz-Pimsner algebras of $C^*$-correspondences fail to generalize to our setting, and discuss what we have instead.

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