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Free Inhomogeneous Wreath Product of Quantum Groups

Quantum Algebra 2025-10-06 v2 Combinatorics Operator Algebras

Abstract

We introduce the free inhomogeneous wreath product of compact matrix quantum groups, which generalizes the free wreath product (Bichon 2004). We use this to present a general technique to determine quantum automorphism groups of connected graphs in terms of their maximal biconnected subgraphs, provided that we have sufficient information about their quantum automorphism groups. We show that this requirement is met for forests, outerplanar graphs, and block graphs leading to algorithms to compute the quantum automorphism groups of these graphs.

Keywords

Cite

@article{arxiv.2504.13826,
  title  = {Free Inhomogeneous Wreath Product of Quantum Groups},
  author = {Josse van Dobben de Bruyn and Amaury Freslon and Prem Nigam Kar and David E. Roberson and Peter Zeman},
  journal= {arXiv preprint arXiv:2504.13826},
  year   = {2025}
}

Comments

27 Pages, 1 Figure