Quantum Automorphism Groups of Hypergraphs

TL;DR

This paper introduces a quantum automorphism group for hypergraphs, extending previous quantum automorphism concepts from graphs to hypergraphs, and demonstrates its action on hypergraph C*-algebras, generalizing earlier graph algebra results.

Contribution

It generalizes quantum automorphism groups from graphs to hypergraphs and shows their action on hypergraph C*-algebras, expanding the scope of quantum symmetry studies.

Findings

Quantum automorphism group for hypergraphs introduced

Action on hypergraph C*-algebras established

Generalizes previous quantum automorphism results for graphs

Abstract

We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as recently defined. In particular, this action generalizes the one on graph C*-algebras by Schmidt-Weber in 2018.