Noncommutative properties of 0-hyperbolic graphs

2025/04/18 by Freslon, Amaury, Meunier, Paul, Pournajafi, Pegah · 3 citations
#05E99 #46L67 (Primary) #46L89 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2504.13808

Abstract

We study several noncommutative properties of 0-hyperbolic graphs. In particular, we prove that 0-hyperbolicity is preserved under quantum isomorphism. We also compute the quantum automorphism groups of 0-hyperbolic graphs and characterise the ones with quantum symmetry.

Citations

• Block structures of graphs and quantum isomorphism
• Quantum automorphism groups of trees
• Quantum and non-signalling graph isomorphisms
• Tsirelson's problem and an embedding theorem for groups arising from non-local games
• Fusion rules for quantum reflection groups
• Free product formulae for quantum permutation groups
• Quantum automorphism groups of small metric spaces
• Free wreath product by the quantum permutation group
• Quantum Symmetry Groups of Finite Spaces
• Sur les assemblages de lignes.

Cited by

• Using Erdős's methods to study Yorke's problems
• Free Inhomogeneous Wreath Product of Quantum Groups

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