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TMF, 2013, Volume 174, Number 3, Pages 364–382 (Mi tmf8380)  

This article is cited in 1 scientific paper (total in 1 paper)

Double extensions of Lie algebras of Kac–Moody type and applications to some Hamiltonian systems

C. Rogerabcd

a Institut Camille Jordan (Laboratoire associé au CNRS UMR 5208), Université Claude Bernard Lyon I, Villeurbanne, France
b Université de Lyon, Lyon, France
c Ecole Centrale de Lyon, Ecully, France
d Institut National des Sciences Appliquées de Lyon, Villeurbanne, France

Abstract: We describe some Lie algebras of the Kac–Moody type, construct their double extensions, central and by derivations{;} we also construct the corresponding Lie groups in some cases. We study the case of the Lie algebra of unimodular vector fields in more detail and use the linear Poisson structure on their regular duals to construct generalizations of some infinite-dimensional Hamiltonian systems, such as magnetohydrodynamics.

Keywords: unimodular vector field, extension of Lie algebra, hydrodynamics, magnetohydrodynamics, coadjoint orbit of Lie algebra

DOI: https://doi.org/10.4213/tmf8380

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English version:
Theoretical and Mathematical Physics, 2013, 174:3, 315–330

Bibliographic databases:

Received: 12.06.2012

Citation: C. Roger, “Double extensions of Lie algebras of Kac–Moody type and applications to some Hamiltonian systems”, TMF, 174:3 (2013), 364–382; Theoret. and Math. Phys., 174:3 (2013), 315–330

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8380
  • http://mi.mathnet.ru/eng/tmf/v174/i3/p364

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Baklouti, “Quadratic Horn-Lie triple systems”, J. Geom. Phys., 121 (2017), 166–175  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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