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Integrability criterion for abelian extensions of Lie groups


Author: Pedram Hekmati
Journal: Proc. Amer. Math. Soc. 138 (2010), 4137-4148
MSC (2010): Primary 22E65, 20K35
DOI: https://doi.org/10.1090/S0002-9939-2010-10423-9
Published electronically: June 9, 2010
MathSciNet review: 2679636
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Abstract: We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras $ \mathfrak{\hat{g}} = \mathfrak{g} \oplus_\omega \mathfrak{a}$ integrates to a corresponding Lie group extension $ A \hookrightarrow \widehat{G} \twoheadrightarrow G$, where $ G$ is connected, simply connected and $ A \cong \mathfrak{a} \slash \Gamma$ for some discrete subgroup $ \Gamma \subseteq \mathfrak{a}$. When $ \pi_1(G)\neq 0$, the kernel $ A$ is replaced by a central extension $ \widehat{A}$ of $ \pi_1(G)$ by $ A$.


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Additional Information

Pedram Hekmati
Affiliation: Department of Theoretical Physics, Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden
Address at time of publication: School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
Email: pedram@kth.se, pedram.hekmati@adelaide.edu.au

DOI: https://doi.org/10.1090/S0002-9939-2010-10423-9
Keywords: Infinite-dimensional Lie theory, abelian extensions
Received by editor(s): January 20, 2010
Received by editor(s) in revised form: February 2, 2010
Published electronically: June 9, 2010
Communicated by: Varghese Mathai
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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