Integrability criterion for abelian extensions of Lie groups

We establish a criterion for when an abelian extension of infinitedimensional Lie algebras ǧ = g ⊕ωa integrates to a corresponding Lie group extension A ǦG G, where G is connected, simply connected and A ̃a/Γ for some discrete subgroup Γ a. When π1(G) not equal 0, the kernel A is replaced by a central extension Ǎ of π1(G) by A. © 2010 American Mathematical Society.Pedram Hekmat