  We discuss the notion of a q-PD-envelope considered by Bhatt and Scholze in
their recent theory of q-crystalline cohomology and explain the relation with
our notion of a divided polynomial twisted algebra. Together with an
interpretation of crystals on the q-crystalline site, that we call q-crystals,
as modules endowed with some kind of stratification, it allows us to associate
a module on the ring of twisted differential operators to any q-crystal. For
simplicity, we explain here only the one dimensional case.
