  A coarse graining operation of spatially homogeneous quantum states based on
an SU(1,1) Lie group structure has recently been proposed in [1] and used in
[2] to compute an explicit renormalisation group flow in the context of loop
quantum cosmology. In this note, we explain the group theoretical origin of
this procedure and generalise previous results based on these insights. We also
highlight how the group theoretical origin of these techniques implies their
immediate generalisation to other Lie groups.
