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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 3, Pages 364–382
DOI: https://doi.org/10.4213/tmf8380 (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
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DOI: https://doi.org/10.4213/tmf8380
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.
Received: 12.06.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 3, Pages 315–330
DOI: https://doi.org/10.1007/s11232-013-0029-x
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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