On C -algebras associated with C -correspondences

By Takeshi Katsura. 2003

274 citations recorded by the source corpus.

Abstract We study C ∗ -algebras arising from C ∗ -correspondences, which were introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our C ∗ -algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem. We also obtain a 6-term exact sequence of K -groups involving the K -groups of our C ∗ -algebras.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55c0a3264df9cfc3c714f0dd7e70f06132a29e7d

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

C*-algebras associated to product systems of hilbert bimodules (2007, methodology): “We then demonstrate that our N OX is compatible with Katsura’s OX [17, 18 ], with the Cuntz-Krieger algebras of finitely aligned higher-rank graphs [30], and with Crisp and Laca’s boundary quotients of Toeplitz algebras [7].”
Operator Algebras for Multivariable Dynamics (2007, methodology): “As such, it sits inside a related Cuntz–Pimsner C*-algebra [45], appropriately defined and studied by Katsura [26] building on an important body of work by Muhly and Solel beginning with [35, 36].”
A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras I, fundamental results (2004, unknown): “borrow many notions from the theory of dynamical systems (see [ Ka3 ]).”
Adding tails to $C^*$-correspondences (2002, methodology): “r many useful conversations regarding these topics. 2. Preliminaries For the most part we will use the notation and conventions of [6], augmenting them when necessary with the innovations of [10] and [11]. Deﬁnition 2.1. If A is a C∗-algebra, then a right Hilbert A-module is a Banach space X togethe”
Co‐universal algebras associated to product systems, and gauge‐invariant uniqueness theorems (2009, methodology): “The basic idea of a co-universal property of a C∗-algebra has appeared before, notably in Exel’s work on Fell bundles [14] which we use in our analysis, in Katsura’s work [22] on C∗-algebras associated to a single bimodule which our work generalizes, and in the work of Laca and Crisp–Laca on Toeplit”
Tensor algebras of C∗-correspondences and their C∗-envelopes (2005, unknown): “O A ] 2 8 D ec”
Semicrossed Products of Operator Algebras by Semigroups (2014, methodology): “However, there are interesting degenerate C*-correspondences, such as C*correspondences arising from non-surjective C*-dynamical systems.”