Integrability Criterion for Abelian Extensions of Lie Groups

Details Integrability Criterion for Abelian Extensions of Lie Groups Integrability Criterion for Abelian Extensions of Lie Groups

2006-11-14

arxiv.org/abs/math/0611431v4

Proc. Amer. Math. Soc., 138(3): 4137-4148, 2010

Mathematics

Differential Geometry

11 pages, 2 figures

Scientific paper

10.1090/S0002-9939-2010-10423-9

We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension $\hat{G}$ of $G$ by $A$, where $G$ is a connected, simply connected Lie group and $A$ is a quotient of its Lie algebra by some discrete subgroup. When $G$ is non-simply connected, the kernel $A$ is replaced by a central extension $\hat{A}$ of $\pi_1(G)$ by $A$.

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