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Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 191–201 (Mi tm3642)  

This article is cited in 6 scientific papers (total in 7 papers)

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

O. K. Sheinman

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

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.”

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515030164

Full text: PDF file (215 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 178–188

Bibliographic databases:

Document Type: Article
UDC: 512.554.3+514.745.82
Received: March 15, 2015

Citation: O. K. Sheinman, “Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 191–201; Proc. Steklov Inst. Math., 290:1 (2015), 178–188

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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846  mathnet  mathscinet  zmath  elib
    2. O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. O. K. Sheinman, “Ispravlenie k rabote “Poluprostye algebry Li i gamiltonova teoriya konechnomernykh uravnenii Laksa so spektralnym parametrom na rimanovoi poverkhnosti” (Tr. MIAN. 2015. T. 290. S. 191–201)”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Sbornik statei, Tr. MIAN, 294, MAIK Nauka/Interperiodika, M., 2016, 325–327  mathnet  crossref  mathscinet  elib
    5. O. K. Sheinman, “Matrix divisors on Riemann surfaces and Lax operator algebras”, Trans. Moscow Math. Soc., 78 (2017), 109–121  mathnet  crossref  elib
    6. O. K. Sheinman, “Certain Reductions of Hitchin Systems of Rank 2 and Genera 2 and 3”, Dokl. Math., 97:2 (2018), 144–146  mathnet  crossref  zmath  isi  scopus
    7. Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47  mathnet  crossref  crossref  isi  elib
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