  We present an explicit realization of abelian extensions of infinite
dimensional Lie groups using abelian extensions of path groups, by generalizing
Mickelsson's approach to loop groups and the approach of
Losev-Moore-Nekrasov-Shatashvili to current groups. We apply our method to
coupled cocycles on current Lie algebras and to Lichnerowicz cocycles on the
Lie algebra of divergence free vector fields.
