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TMF, 2010, Volume 162, Number 2, Pages 179–195 (Mi tmf6463)  

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

Symmetry algebras of Lagrangian Liouville-type systems

A. V. Kiselev, J. W. van de Leur

Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

Abstract: We calculate the generators and commutation relations explicitly for higher symmetry algebras of a class of hyperbolic Lagrangian systems of Liouville type, in particular, for two-dimensional Toda chains associated with semisimple complex Lie algebras.

Keywords: symmetry, two-dimensional Toda chain, Liouville-type system, Hamiltonian hierarchy, bracket

DOI: https://doi.org/10.4213/tmf6463

Full text: PDF file (647 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2010, 162:2, 149–162

Bibliographic databases:

Received: 26.02.2009
Revised: 18.05.2009

Citation: A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, TMF, 162:2 (2010), 179–195; Theoret. and Math. Phys., 162:2 (2010), 149–162

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kiselev A.V., van de Leur J.W., “A family of second Lie algebra structures for symmetries of a dispersionless Boussinesq system”, Journal of Physics A-Mathematical and Theoretical, 42:40 (2009), 404011  crossref  mathscinet  zmath  isi  scopus
    2. A. V. Kiselev, J. W. van de Leur, “Variational Lie algebroids and homological evolutionary vector fields”, Theoret. and Math. Phys., 167:3 (2011), 772–784  mathnet  crossref  crossref  adsnasa  isi
    3. Hussin V., Kiselev A.V., “A convenient criterion under which $\mathbb Z_2$-graded operators are Hamiltonian”, Physical and Mathematical Aspects of Symmetry: Proceedings of the 28th International Colloquium on Group-Theoretical Methods in Physics, J. Phys.: Conf. Ser., 284, 2011, 012035  crossref  adsnasa  isi  scopus
    4. Kiselev A.V., “Homological evolutionary vector fields in Korteweg–de Vries, Liouville, Maxwell, and several other models”, 7th International Conference on Quantum Theory and Symmetries (QTS7), J. Phys.: Conf. Ser., 343, 2012, 012058  crossref  adsnasa  isi  scopus
    5. Kiselev A.V. Krutov A.O., “Non-Abelian Lie Algebroids Over Jet Spaces”, J. Nonlinear Math. Phys., 21:2 (2014), 188–213  crossref  mathscinet  isi  scopus
    6. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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