Isometric actions of compact quantum groups on graph C*-algebras

Abstract

For a strongly connected directed graph $\hat{I}›$, it is shown that the quantum automorphism group of $\hat{I}›$ acts isometrically in the sense of D. Goswami et al. on the spectral triple $(C^{\ast }(\hat{I}›),L^2(\hat{I}{›}^{\infty },M),D)$ constructed by Farsi et al.. It is also shown that the natural action of $U_n^{+}$ is not isometric on the Cuntz algebra ${\mathcal{O}}_n$.

21 pages