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Quantum automorphism groups of trees

  • Josse van Dobben de Bruyn

    Technical University of Denmark, Kongens Lyngby, Denmark

  • Prem Nigam Kar

    Technical University of Denmark, Kongens Lyngby, Denmark

  • David E. Roberson

    Technical University of Denmark, Kongens Lyngby, Denmark; University of Copenhagen, Copenhagen, Denmark

  • Simon Schmidt

    Ruhr-Universität Bochum, Bochum, Germany

  • Peter Zeman

    Technical University of Denmark, Kongens Lyngby, Denmark
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Abstract

We give a characterization of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a quantum version of Jordan’s theorem for the automorphism groups of trees. We use ideas from algebraic combinatorics, quantum groups, and quantum information theory. This is one of the first characterizations of quantum automorphism groups of a natural class of graphs with quantum symmetry.

Cite this article

Josse van Dobben de Bruyn, Prem Nigam Kar, David E. Roberson, Simon Schmidt, Peter Zeman, Quantum automorphism groups of trees. J. Noncommut. Geom. (2025), published online first

DOI 10.4171/JNCG/607