  The notion of inner linear Hopf algebra is a generalization of the notion of
discrete linear group. In this paper, we prove two general results that enable
us to enlarge the class of Hopf algebras that are known to be inner linear: the
first one is a characterization by using the Hopf dual, while the second one is
a stability result under extensions. We also discuss the related notion of
inner unitary Hopf *-algebra.
