Quantum symmetry of graph C*-algebras at critical inverse temperature

TL;DR

This paper introduces a new notion of quantum automorphism groups for graph C*-algebras at critical inverse temperature, linking them to existing categories and providing a framework for understanding quantum symmetries in this setting.

Contribution

It defines quantum automorphism groups of graph C*-algebras at critical inverse temperature and connects these to previously established categories and structures.

Findings

The category of CQG's preserving the KMS state matches existing categories for certain graphs.

An orthogonal filtration on Cuntz algebra aligns with the quantum automorphism category.

The framework extends quantum symmetry concepts to graph C*-algebras at critical temperature.

Abstract

We give a notion of quantum automorphism group of graph C*-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear action in the sense of [11] and preserving the KMS state at critical inverse temperature. We show that this category for a certain KMS state at critical inverse temperature coincides with the category introduced in [11] for a class of graphs. We also introduce an orthogonal filtration on Cuntz algebra with respect to the unique KMS state and show that the category of CQG's preserving the orthogonal filtration coincides with the category introduced in this paper.