Neeb KH (2002)
Publication Type: Journal article, Original article
Publication year: 2002
Publisher: Springer Verlag (Germany)
Book Volume: 73
Pages Range: 175-219
Journal Issue: 1
We call a central Z-extension of a group G weakly universal for an Abelian group A if the correspondence assigning to a homomorphism Z→A the corresponding A-extension yields a bijection of extension classes. The main problem discussed in this paper is the existence of central Lie group extensions of a connected Lie group G which is weakly universal for all Abelian Lie groups whose identity components are quotients of vector spaces by discrete subgroups. We call these Abelian groups regular. In the first part of the paper we deal with the corresponding question in the context of topological, Fréchet, and Banach–Lie algebras, and in the second part we turn to the groups. Here we start with a discussion of the weak universality for discrete Abelian groups and then turn to regular Lie groups A. The main results are a Recognition and a Characterization Theorem for weakly universal central extensions.
APA:
Neeb, K.H. (2002). Universal Central Extensions of Lie Groups. Acta Applicandae Mathematicae, 73(1), 175-219. https://dx.doi.org/10.1023/A:1019743224737
MLA:
Neeb, Karl Hermann. "Universal Central Extensions of Lie Groups." Acta Applicandae Mathematicae 73.1 (2002): 175-219.
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