  Continuing our research on extensions of locally compact quantum groups, we
give a classification of all cocycle matched pairs of Lie algebras in small
dimensions and prove that all of them can be exponentiated to cocycle matched
pairs of Lie groups. Hence, all of them give rise to locally compact quantum
groups by the cocycle bicrossed product construction. We also clarify the
notion of an extension of locally compact quantum groups by relating it to the
concept of a closed normal quantum subgroup and the quotient construction.
Finally, we describe the infinitesimal objects of locally compact quantum
quantum groups with 2 and 3 generators - Hopf *-algebras and Lie bialgebras.
