English

On quantum Cayley graphs

Operator Algebras 2024-12-11 v2 Quantum Algebra

Abstract

We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side and suggest an extension of the theory of quantum graphs to the infinite dimensional case. Then we use this framework to introduce quantum graphs associated to discrete quantum groups, leading to a new definition of a quantum Cayley graph.

Keywords

Cite

@article{arxiv.2306.15315,
  title  = {On quantum Cayley graphs},
  author = {Mateusz Wasilewski},
  journal= {arXiv preprint arXiv:2306.15315},
  year   = {2024}
}

Comments

32 pages, this is the author accepted manuscript

R2 v1 2026-06-28T11:15:28.824Z