Abelian extensions of infinite-dimensional Lie groups
Neeb KH (2004)
Publication Type: Journal article, Original article
Publication year: 2004
Journal
Publisher: University of Luxembourg
Book Volume: 15
Pages Range: 69-194
Abstract
In the present paper we study abelian extensions of connected Lie groups G modeled on locally convex spaces by smooth G-modules A. We parametrize the extension classes by a suitable cohomology group H2s(G,A) defined by locally smooth cochains and construct an exact sequence that describes the difference between H2s(G,A) and the corresponding continuous Lie algebra cohomology space $H^2_c(\g,\a)$. The obstructions for the integrability of a Lie algebra extensions to a Lie group extension are described in terms of period and flux homomorphisms. We also characterize the extensions with global smooth sections resp. those given by global smooth cocycles. Finally we apply the general theory to extensions of several types of diffeomorphism groups.
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How to cite
APA:
Neeb, K.H. (2004). Abelian extensions of infinite-dimensional Lie groups. Travaux mathématiques, 15, 69-194.
MLA:
Neeb, Karl Hermann. "Abelian extensions of infinite-dimensional Lie groups." Travaux mathématiques 15 (2004): 69-194.
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