  It is an open question whether fluctuations at the Planck scale in a
non-perturbative theory of quantum gravity behave in such a way that the
resulting semi-classical geometry can be modelled by a space that admits
(approximate) Killing symmetries. We have investigated whether the notion of
approximate Killing vector fields is suitable to address this question in
lattice theories of quantum gravity, such as (Causal) Dynamical Triangulations.
We show that it is possible to construct quantum observables related to
approximate Killing vector fields using the framework of Discrete Exterior
Calculus. We have evaluated the expectation value of one particular choice of
observable on three toy models of two-dimensional quantum gravity.
