Free Group Algebras in Certain Division Rings

LetDbe a division ring with centrek. We show thatDcontains thek-group algebra of the free group on two generators whenDis the ring of fractions of a suitable skew polynomial ring, or it is generated by a polycyclic-by-finite group which is not abelian-by-finite, or it is the ring of fractions of the universal enveloping algebra of a finite-dimensional Lie algebra of characteristic zero.