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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 by an abelian group
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 Fréchet-Lie groups. The exact sequence
encodes in particular precise obstructions for a given Lie algebra...
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