Realizations of real low-dimensional Lie algebras

From MaRDI portal
Publication:4466334

DOI10.1088/0305-4470/36/26/309zbMath1040.17021arXivmath-ph/0301029OpenAlexW3100656718WikidataQ60395404 ScholiaQ60395404MaRDI QIDQ4466334

Roman O. Popovych, Maxim Lutfullin, Maryna Nesterenko, Vyacheslav M. Boyko

Publication date: 9 June 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0301029




Related Items

\(J\)-trajectories in 4-dimensional solvable Lie group \(\mathrm{Sol}_0^4\)Contractions of low-dimensional Lie algebrasA fixed point result and the stability problem in Lie superalgebrasDEFORMATIONS OF FOUR-DIMENSIONAL LIE ALGEBRASSecond-order systems of ODEs admitting three-dimensional Lie algebras and integrabilityA note on four-dimensional symmetry algebras and fourth-order ordinary differential equationsConstruction of polynomial algebras from intermediate Casimir invariants of Lie algebrasA group theoretical identification of integrable cases of the Liénard-type equation ẍ+f(x)ẋ+g(x)=. I. Equations having nonmaximal number of Lie point symmetriesJacobi-Lie Hamiltonian Systems on Real Low-Dimensional Jacobi-Lie Groups and their Lie SymmetriesClassification of homogeneous CR-manifolds in dimension 4Composition of Lie Group Elements from Basis Lie Algebra ElementsLie group classification of first-order delay ordinary differential equationsEmbedding algorithms and applications to differential equationsIntegrating of systems of two second-order ordinary differential equations with a small parameter that admit four essential operatorsOn nilpotent and solvable Lie algebras of derivationsExtended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equationLowest-dimensional example on non-universality of generalized Inönü-Wigner contractionsExtended symmetry analysis of generalized Burgers equationsNambu structures on four-dimensional real Lie groups and related superintegrable systemsOn the (non)removability of spectral parameters in \(\mathbb{Z}_{2}\)-graded zero-curvature representations and its applicationsDeformations of Yang-Baxter operators via \(n\)-Lie algebra cohomologyPoint and generalized symmetries of the heat equation revisitedCosmological quantum states of de Sitter-Schwarzschild are static patch partition functionsKinematical invariance groups of the 3d Schrödinger equations with position dependent massesOn the classification of 3-dimensional complex hom-Lie algebrasA new look at Lie algebrasIntegrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groupsMaster partial differential equations for a type II hidden symmetryThree-dimensional dynamical systems admitting nonlinear superposition with three-dimensional Vessiot-Guldberg-Lie algebrasAre all classical superintegrable systems in two-dimensional space linearizable?Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equationGalilei's relativity principle for a system of reaction-convection-diffusion equationsAlgebraic linearization criteria for systems of ordinary differential equationsInvariant Control Systems on Lie GroupsInvariant Poisson–Nijenhuis structures on Lie groups and classification\(r\)-harmonic and complex isoparametric functions on the Lie groups \(\mathbb{R}^m\ltimes\mathbb{R}^n\) and \(\mathbb{R}^m\times\text{H}^{2n+1}\)Symmetries of second-order systems of ODEs and integrabilityGeneralization of the algebraic method of group classification with application to nonlinear wave and elliptic equationsSystems of reaction-convection-diffusion equations invariant under Galilean algebrasControl systems on three-dimensional Lie groups: equivalence and controllabilityExtended symmetry analysis of an isothermal no-slip drift flux modelHidden symmetry algebra and construction of quadratic algebras of superintegrable systemsReduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizationsSingular invariant structures for Lie algebras admitted by a system of second-order ODEsRealizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equationsExtended symmetry analysis of two-dimensional degenerate Burgers equationTransformation groups on real plane and their differential invariantsInvariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elementsIntegrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebrasCOMMENT ON "STABILITY OF (α, β, γ)-DERIVATIONS ON LIE C*-ALGEBRAS" [M. ESHAGHI GORDJI AND N. GHOBADIPOUR, INT. J. GEOM.METHODS MOD. PHYS. 7(7) (2010) 1–10] ⋮ Quadratic Hamilton-Poisson systems in three dimensions: equivalence, stability, and integrationOn \((\alpha,\beta,\gamma)\)-derivations of Lie algebras and corresponding invariant functionsComplete point symmetry group of the barotropic vorticity equation on a rotating sphereOn symmetries of the Fokker-Planck equationThe global extension problem, crossed products and co-flag non-commutative Poisson algebrasIntegrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systemsSymmetry breaking of systems of linear second-order ordinary differential equations with constant coefficients\(E_{6(6)}\) exceptional Drinfel'd algebrasLie subalgebras of differential operators in one variableSTABILITY OF (α, β, γ)-DERIVATIONS ON LIE C*-ALGEBRASTwisted cocycles of Lie algebras and corresponding invariant functionsJacobi and Poisson algebrasEnhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivityOn the ineffectiveness of constant rotation in the primitive equations and their symmetry analysisCanonical forms and their integrability for systems of three 2nd-order ODEsSymmetry analysis of a system of modified shallow-water equationsLie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetryPoisson-Lie U-duality in exceptional field theorySolvable Lie algebras of vector fields and a Lie's conjectureModuli spaces of low dimensional real Lie algebrasClassification of the realizations of Lie algebras for the vector fields on a circleApproximate \((\alpha ,\beta ,\gamma )\)-derivation on random Lie \(C^*\)-algebrasApproximate reciprocal Lie \(\star \)-derivationsLie symmetry analysis and exact solutions of the quasigeostrophic two-layer problemSecond-order delay ordinary differential equations, their symmetries and application to a traffic problem