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Non-abelian extensions of infinite-dimensional Lie groups

Karl-Hermann Neeb (2007)

Annales de l’institut Fourier

In this article we study non-abelian extensions of a Lie group G modeled on a locally convex space by a Lie group N . The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions S of G on N . If S is given, we show that the corresponding set Ext ( G , N ) S of extension classes is a principal homogeneous space of the locally smooth cohomology group H s s 2 ( G , Z ( N ) ) S . To each S a locally smooth obstruction class χ ( S ) in a suitably defined cohomology group H s s 3 ( G , Z ( N ) ) S is defined....

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