Representations of Cuntz-Pimsner algebras

By N. Fowler, P. Muhly, Iain Raeburn. 2003

142 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e6325f3c52b276191e199efca9193d2eb657f57

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

Citations in the corpus

Ideal structure of C∗-algebras associated with C∗-correspondences (2003, background): “In [Kajiwara et al. 1998; Fowler et al. 2003; Schweizer 2001], a positively invariant ideal is called X -invariant.”
Operator Algebras for Multivariable Dynamics (2007, background): “This was further analyzed in [18].”
The ideal structure of the $C\sp *$-algebras of infinite graphs (2001, background): “First, they provide good test problems in the general theories of groupoid algebras [16, 15, 18], Cuntz-Pimsner algebras [19, 21, 13, 9, 10 ], and partial crossed products [6, 8]. Second, the simple graph algebras provide a rich family of accessible models for purely infinite simple C ∗-algebras.”
Isomorphisms of algebras associated with directed graphs (2003, methodology): “We would like to thank the referee for several constructive suggestions on the initial draft and for bringing to our attention the work in [8, 9].”
C*-algebras associated to product systems of hilbert bimodules (2007, methodology): “In the spirit of Coburn’s Theorem for the classical Toeplitz algebra [5], Fowler and Raeburn proved a uniqueness theorem for TX [16, Theorem 3.1].”
A construction of $C^*$-algebras from $C^*$-correspondences (2003, background): “Finally, we emphasize that even if one starts with a C ∗-correspondence with an injective and non-degenerate left action, one needs to work with C ∗-correspondences with non-injective or degenerate left actions, in order to know about the ideals and quotients of its C ∗-algebra (see [ FMR , K2]).”
Tensor algebras of C∗-correspondences and their C∗-envelopes (2005, result): “This improves earlier results of Muhly and Solel [13] and Fowler, Muhly and Raeburn [5], who came to the same conclusion under the additional hypothesis that X is strict and faithful.”
The primitive ideal space of the $C^{*}$-algebras of infinite graphs (2002, background): “Watatani [15], and Fowler, Muhly and Raeburn [ 8 ].”
Adding tails to $C^*$-correspondences (2002, unknown): “The first author was supported by NSF Grant DMS-0070405 and the second author was supported by NSF Postdoctoral Fellowship DMS-0201960.”
Dilation theory, commutant lifting and semicrossed products (2011, background): “The C*-envelope is the Cuntz-Pimsner algebra O(E) [42, 29, 34].”
Co‐universal algebras associated to product systems, and gauge‐invariant uniqueness theorems (2009, background): “In an impressive array of papers [21, 22, 23] Katsura, drawing on insight from graph algebras and drawing on results on quotients of Cuntz-Pimsner algebras developed in [19], not only expanded Pimsner’s theory of C∗-algebras associated with Hilbert bimodules beyond the case of isometric left actions”