Central extensions of infinite-dimensional Lie groups

The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group G by an abelian group Z whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Frechet-Lie groups. The exact sequence encodes in particular precise obstructions for a given Lie algebra cocycle to correspond to a locally group cocycle.