scholarly journals Quasigraded Lie Algebras and Modified Toda Field Equations

2006 ◽  
Author(s):  
Taras V. Skrypnyk
Keyword(s):  
Lie Algebras ◽  
Field Equations ◽  
Quasigraded Lie Algebras

DEFORMATIONS OF LOOP ALGEBRAS AND CLASSICAL INTEGRABLE SYSTEMS: FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

2004 ◽  
Vol 16 (07) ◽  
pp. 823-849 ◽  
Author(s):  
T. SKRYPNYK
Keyword(s):  
Lie Algebras ◽  
Hamiltonian Systems ◽  
Spectral Parameter ◽  
Integrable Systems ◽  
Integrable Hamiltonian Systems ◽  
Infinite Dimensional ◽  
Loop Algebras ◽  
Finite Dimensional ◽  
Quasigraded Lie Algebras ◽  
Classical Integrable

We construct a family of infinite-dimensional quasigraded Lie algebras, that could be viewed as deformation of the graded loop algebras and admit Kostant–Adler scheme. Using them we obtain new integrable hamiltonian systems admitting Lax-type representations with the spectral parameter.

TOROIDAL LIE ALGEBRAS AND SOME DIFFERENTIAL EQUATIONS OF TODA TYPE

2010 ◽  
Vol 09 (06) ◽  
pp. 1015-1031
Author(s):  
YOUJUN TAN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Hamiltonian Formalism ◽  
Differential Polynomial ◽  
Field Equations ◽  
Partial Differential ◽  
Polynomial Algebras ◽  
Recursive System

We deduce a recursive system of partial differential equations from the toroidal Lie algebra associated to a simple Lie algebra. Such a recursive system starts from the corresponding classical Toda field equations. For each truncated system we describe its Hamiltonian formalism using Gel'fand–Dikii's differential polynomial algebras, and some nontrivial local integrals are given.

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