# CQG: Uniqueness of the Representation in Homogeneous Isotropic Loop Quantum Cosmology

## Main Content

We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) used in the literature is the GNS-representation associated to the unique state on the reduced quantum holonomy-flux ∗-algebra that is invariant under residual diffeomorphisms -- *both* when the standard, simpler algebra with holonomies along only straight edges is used, as well as when one uses the larger algebra (studied by Fleischhack) which includes curved edges and thus would seem to be more faithful to full loop quantum gravity. In order for the residual diffeomorphisms to have a well-defined action on the quantum algebra, we have let them act on the fiducial cell as well as on the dynamical variables, thereby recovering covariance.