Isometry groups of inductive limits of metric spectral triples and Gromov–Hausdorff convergence

Abstract In this paper, we study the groups of isometries and set bi‐Lipschitz automorphisms spectral triples from a metric viewpoint, in propinquity framework Latrémolière. particular, prove that these sets are compact automorphism group triple ‐algebra with respect to Monge–Kantorovich metric, which induces topology pointwise convergence. We then necessary sufficient condition for convergence actions various isometries, sense covariant version Gromov–Hausdorff propinquity, noncommutative analogue distance, when working context inductive limits quantum spaces triples. illustrate our work examples including AF algebras solenoids.