Maier P, Neeb KH (2003)
Publication Type: Journal article, Original article
Publication year: 2003
Publisher: Springer Verlag (Germany)
Book Volume: 326
Pages Range: 367-415
Journal Issue: 2
DOI: 10.1007/s00208-003-0425-x
In this paper we study central extensions of the identity component G of the Lie group C ∞ (M,K) of smooth maps from a compact manifold M into a Lie group K which might be infinite-dimensional. We restrict our attention to Lie algebra cocycles of the form ω(ξ,η)=[κ(ξ,dη)], where κ:𝔨×𝔨→Y is a symmetric invariant bilinear map on the Lie algebra 𝔨 of K and the values of ω lie in Ω1(M,Y)/dC ∞ (M,Y). For such cocycles we show that a corresponding central Lie group extension exists if and only if this is the case for M=𝕊1. If K is finite-dimensional semisimple, this implies the existence of a universal central Lie group extension
APA:
Maier, P., & Neeb, K.H. (2003). Central extensions of current groups. Mathematische Annalen, 326(2), 367-415. https://doi.org/10.1007/s00208-003-0425-x
MLA:
Maier, Peter, and Karl Hermann Neeb. "Central extensions of current groups." Mathematische Annalen 326.2 (2003): 367-415.
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