Quantum Symmetry of Graph C*-algebras associated with connected Graphs

TL;DR

This paper introduces a new concept of quantum automorphism groups for finite, connected graph C*-algebras, compares it with existing notions, and computes quantum symmetries for specific examples.

Contribution

It defines a novel quantum automorphism group for graph C*-algebras and establishes its relation to Banica's quantum automorphism group, including concrete symmetry computations.

Findings

Quantum automorphism group is a quantum subgroup of Banica's group under certain conditions.

Quantum symmetries for specific graph C*-algebras have been explicitly computed.

The new notion applies to finite, connected graphs without multiple edges or loops.

Abstract

We define a notion of quantum automorphism group of Graph C*-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of underlying directed graph in the sense of T. banica is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph C*-algebras have been computed.