Quantum automorphism groups of trees
Quantum Algebra
2023-11-09 v1 Combinatorics
Abstract
We give a characterisation 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. This is one of the first characterisations of quantum automorphism groups of a natural class of graphs with quantum symmetry.
Cite
@article{arxiv.2311.04891,
title = {Quantum automorphism groups of trees},
author = {Josse van Dobben de Bruyn and Prem Nigam Kar and David E. Roberson and Simon Schmidt and Peter Zeman},
journal= {arXiv preprint arXiv:2311.04891},
year = {2023}
}