Cuntz-Pimsner algebras for subproduct systems

Abstract

In this paper we generalize the notion of Cuntz-Pimsner algebras of $C^{\ast }$-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 $C^{\ast }$-correspondences fail to generalize to our setting, and discuss what we have instead.

33 pages

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Cited by in corpus (10)

• Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball
• CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond
• Operator algebras and subproduct systems arising from stochastic matrices
• Gysin sequences and SU(2)-symmetries of C*-algebras
• On operator algebras associated with monomial ideals in noncommuting variables
• Berezin quantization of noncommutative projective varieties
• Toeplitz extensions in noncommutative topology and mathematical physics
• Subproduct systems with quantum group symmetry
• Tensor algebras of subproduct systems and noncommutative function theory
• The Motzkin subproduct system