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

arXiv comment14 pages

Cited by in corpus (6)

• Braided quantum symmetries of graph ${\mathrm{C}}^{\ast }$-algebras
• Rigidity on Quantum Symmetry for a Certain Class of Graph C*-algebras
• Invariance of KMS states on graph C*-algebras under classical and quantum symmetry
• On outer automorphisms of certain graph $C^{\ast }$-algebras
• Quantum isomorphism of $2$-graphs
• Equivariant ${\mathrm{C}}^{\ast }$-correspondences and compact quantum group actions on Pimsner algebras