Quantum symmetry of graph $C^{\ast }$-algebras at critical inverse temperature
Volume 256 / 2021
Abstract
We study quantum automorphism groups of graph $C^{\ast }$-algebras without sinks at critical inverse temperature. This is naturally defined to be the universal object in the category of compact quantum groups having a linear action in the sense of our previous paper [Infin. Dimens. Anal. Quantum Probab. Related Topics 21 (2018)] and preserving a 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 the previous paper for a large class of graphs. Moreover, an orthogonal filtration on the Cuntz algebra with respect to the unique KMS state is introduced and it is shown that the category of compact quantum groups preserving the orthogonal filtration coincides with the category introduced in this paper.
