  Some general criteria to produce explicit free algebras inside the division
ring of fractions of skew polynomial rings are presented. These criteria are
applied to some special cases of division rings with natural involutions,
yielding, for instance, free subalgebras generated by symmetric elements both
in the division ring of fractions of the group algebra of a torsion free
nilpotent group and in the division ring of fractions of the first Weyl
algebra.
