Geodesic
Hierarchies of finite-dimensional Lax equations with a~spectral parameter on a~Riemann surface and semisimple Lie algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 527-544

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Based on $\mathbb Z$-gradings of semisimple Lie algebras and invariant polynomials on them, we construct hierarchies of Lax equations with a spectral parameter on a Riemann surface and prove the commutativity of the corresponding flows.
Keywords: Lax operator algebra, hierarchy, semisimple Lie algebra, Riemann surface.
Mots-clés : Lax equation 
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     author = {O. K. Sheinman},
     title = {Hierarchies of finite-dimensional {Lax} equations with a~spectral parameter on {a~Riemann} surface and semisimple {Lie} algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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O. K. Sheinman. Hierarchies of finite-dimensional Lax equations with a~spectral parameter on a~Riemann surface and semisimple Lie algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 527-544. http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a8/