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SIGMA, 2006, Volume 2, 043, 14 pages (Mi sigma71)  

This article is cited in 5 scientific papers (total in 5 papers)

Quasigraded Lie Algebras and Modified Toda Field Equations

Taras V. Skrypnykab

a Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., Kyiv, 03143 Ukraine
b Institute of Mathematics, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine

Abstract: We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in “principal” gradation and admit Kostant–Adler–Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda field equations for all series of classical matrix Lie algebras $\mathfrak g$.

Keywords: infinite-dimensional Lie algebras; soliton equations

DOI: https://doi.org/10.3842/SIGMA.2006.043

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Full text: http://emis.mi.ras.ru/.../Paper043
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Bibliographic databases:

ArXiv: nlin.SI/0604032
MSC: 37K05; 37K30
Received: October 31, 2005; in final form March 3, 2006; Published online April 16, 2006
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Citation: Taras V. Skrypnyk, “Quasigraded Lie Algebras and Modified Toda Field Equations”, SIGMA, 2 (2006), 043, 14 pp.

Citation in format AMSBIB
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\by Taras V.~Skrypnyk
\paper Quasigraded Lie Algebras and Modified Toda Field Equations
\jour SIGMA
\yr 2006
\vol 2
\papernumber 043
\totalpages 14
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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. Skrypnyk, T, “Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras”, Journal of Mathematical Physics, 47:6 (2006), 063509  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Skrypnyk, T, “New non-skew symmetric classical r-matrices and 'twisted' quasigraded Lie algebras”, Journal of Physics A-Mathematical and Theoretical, 40:7 (2007), 1611  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Blaszak, M, “Classical R-matrix theory for bi-Hamiltonian field systems”, Journal of Physics A-Mathematical and Theoretical, 42:40 (2009), 404002  crossref  mathscinet  zmath  isi  scopus
    4. Skrypnyk T., “Quasigraded Bases in Loop Algebras and Classical Rational R-Matrices”, J. Math. Phys., 53:8 (2012), 083501  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Skrypnyk T., “Reduction in Soliton Hierarchies and Special Points of Classical R-Matrices”, J. Geom. Phys., 130 (2018), 260–287  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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