On amplified graph C*-algebras as cores of Cuntz-Krieger algebras

2025/10/18 by D'Andrea, Francesco, Zegers, Sophie Emma
#46L67 #46L80 #46L85 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2510.16430

Abstract

Given a finite directed acyclic graph R, we construct from it two graphs E_R and F_R, one by adding a loop at every vertex of R and one by replacing every arrow of R by countably infinitely many arrows. We show that the graph C*-algebra C^*(F_R) is isomorphic to the AF core of C^*(E_R). Examples include C*-algebras of a quantum flag manifolds and quantum teardrops. We discuss in detail the quantum Grassmannian Gr_q(2,4) and use our description as AF core to study its CW-structure.

Citations

• On the K-theory of the AF core of a graph C*-algebra
• The K-theory type of quantum CW-complexes
• Strongly graded Leavitt path algebras
• Graph algebras
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• Strongly graded groupoids and strongly graded Steinberg algebras
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• The K-theory of twisted multipullback quantum odd spheres and complex\n projective spaces
• Free actions of compact quantum group on unital C*-algebras
• The K-theory of the triple-Toeplitz deformation of the complex\n projective plane
• The graded structure of Leavitt Path algebras
• The ideal structure of the C*-algebras of infinite graphs
• Computing K-theory and Ext for graph C*-algebras
• Pullback and Pushout Constructions in C*-Algebra Theory

Related

• On the K-theory of the AF core of a graph C*-algebra
• Quantum Cuntz-Krieger algebras
• Quantum edge correspondences and quantum Cuntz-Krieger algebras
• A route to quantum computing through the theory of quantum graphs
• On the K-theory of graph C*-algebras