A construction of $C^*$-algebras from $C^*$-correspondences
By Takeshi Katsura. 2003
103 citations recorded by the source corpus.
We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/22f2d20358eec1fd6ff06421cd37f5d96ac74271
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- C*-algebras associated to product systems of hilbert bimodules (2007, methodology): “Just as the uniqueness theorems of [2] informed the work of Fowler, Muhly and Raeburn [14] and of Katsura [ 17 , 18], the uniqueness theorems of [30] provide an informative model for C ∗-algebras associated to compactly aligned product systems.”
- On C -algebras associated with C -correspondences (2003, methodology): “K(X) −−−→ ψt X B [0,1] −−−→A/JX −−−→0. ON C∗-ALGEBRAS ASSOCIATED WITH C∗-CORRESPONDENCES 13 From this diagram, we have the equivalence (ii) ⇐⇒(iii). Finally, the equivalence (iii) ⇐⇒(iv) was shown in [Ka2]. 6. The gauge-invariant uniqueness theorem In this section, we will give conditions for repres”
- Adding tails to $C^*$-correspondences (2002, methodology): “r, and for 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 ”
- Ideal structure of C∗-algebras associated with C∗-correspondences (2003, background): “zations of endomorphisms, a natural problem is to define “crossed products” by C∗-correspondences. There are plenty of evidence that the construction of the C∗-algebra O X from a C∗-correspondence Xin [K4] is the right one. One piece of evidence is that this generalizes many constructions which were ”
- A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras IV, pure infiniteness (2008, unknown): “In [Ka2], we introduce a way to associate a C ∗ -algebra O(E) to a topological graph E, which uses a construction of C ∗ algebras from C ∗ -correspondences (see [ Ka5 ]).”