The path group construction of Lie group extensions"
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