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Double extensions of Lie algebras of Kac–Moody type and applications to some Hamiltonian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 3, pp. 364-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : coadjoint orbit of Lie algebra. 
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C. Roger. Double extensions of Lie algebras of Kac–Moody type and applications to some Hamiltonian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 3, pp. 364-382. http://geodesic.mathdoc.fr/item/TMF_2013_174_3_a1/

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