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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Integrability criterion for abelian extensions of Lie groups
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by Pedram Hekmati PDF
Proc. Amer. Math. Soc. 138 (2010), 4137-4148 Request permission

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 $A \cong \mathfrak {a} / \Gamma$ 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
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2679636