Lie algebras of slow growth and Klein-Gordon PDE

DOI10.1007/s10468-018-9794-4zbMath1440.17023OpenAlexW2802062200WikidataQ129872939 ScholiaQ129872939MaRDI QIDQ1792606

Dmitry V. Millionshchikov

Publication date: 12 October 2018

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-018-9794-4

zbMATH Keywords

sine-Gordon equationGelfand-Kirillov dimensionloop algebraKac-Moody algebraBell polynomialhyperbolic PDETzitzeica equationcharacteristic Lie algebranaturally graded Lie algebra

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Applications of Lie algebras and superalgebras to integrable systems (17B80) Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetries, invariants, etc. in context of PDEs (35B06) Second-order semilinear hyperbolic equations (35L71)

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An algebraic criterion of the Darboux integrability of differential-difference equations and systems ⋮ Lax pair for a novel two-dimensional lattice ⋮ Residually solvable extensions of pro-nilpotent Leibniz superalgebras ⋮ A classification algorithm for integrable two-dimensional lattices via Lie-Rinehart algebras ⋮ On construction of Darboux integrable discrete models ⋮ Algebraic properties of quasilinear two-dimensional lattices connected with integrability ⋮ Classification of a subclass of quasilinear two-dimensional lattices by means of characteristic algebras ⋮ On a class of 2D integrable lattice equations ⋮ Characteristic algebras and integrable exponential systems ⋮ Polynomial Lie algebras and growth of their finitely generated Lie subalgebras ⋮ Integrability conditions for two-dimensional Toda-like equations

Cites Work

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• Classification of graded Lie algebras with two generators
• Theory of group representations and integration of nonlinear dynamical systems
• The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems
• On the characteristic Lie algebras for equations \(u_{xy} = f(u, u_x)\)
• On the complete integrability of a nonlinear system of partial differential equations in two-dimensional space
• Two-dimensional nonlinear system of differential equations x//alpha,//\(z_ z-\)=exp(kx)//alpha
• Classification of simple graded Lie algebras of finite growth
• Lie algebraic approaches to classical partition identities
• Construction of the affine Lie algebra \(A^{(1)}_1\)
• Narrow algebras and groups
• General solutions to the 2D Liouville equation
• Rigid Carnot algebras: a classification
• Sur les corps liés aux algèbres enveloppantes des algèbres de Lie
• Exactly integrable hyperbolic equations of Liouville type
• Polynomial Lie algebras and the Zelmanov-Shalev theorem
• SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH
• Differential Forms on General Commutative Algebras

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