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Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface

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Abstract

The Hamiltonian property and integrability of the Lax equations with spectral parameter on a Riemann surface are considered. The operators of Lax pairs are meromorphic functions of special form on a Riemann surface of arbitrary positive genus with values in an arbitrary semisimple Lie algebra. The study combines the theory of Lax equations with spectral parameter on a Riemann surface, as proposed by I.M. Krichever in 2001, with a “group-theoretic approach.”

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  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    O. K. Sheinman

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  1. O. K. Sheinman
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Original Russian Text © O.K. Sheinman, 2015, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Vol. 290, pp. 191–201.

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Sheinman, O.K. Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface. Proc. Steklov Inst. Math. 290, 178–188 (2015). https://doi.org/10.1134/S0081543815060164

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  • DOI: https://doi.org/10.1134/S0081543815060164

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