Quadratic algebra contractions and second-order superintegrable systems

DOI10.1142/S0219530514500377zbMath1300.22013arXiv1401.0830MaRDI QIDQ2925316

Willard jun. Miller, Ernest G. Kalnins

Publication date: 21 October 2014

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.0830

zbMATH Keywords

quadratic algebrascontractionssuperintegrable systemsAskey scheme

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Applications of Lie groups to the sciences; explicit representations (22E70) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Representation theory of associative rings and algebras (16G99)

Related Items (10)

Bôcher contractions of conformally superintegrable Laplace equations ⋮ AdS perturbations, isometries, selection rules and the Higgs oscillator ⋮ Projectively equivalent 2-dimensional superintegrable systems with projective symmetries ⋮ Separation equations for 2D superintegrable systems on constant curvature spaces ⋮ Contractions of degenerate quadratic algebras, abstract and geometric ⋮ Toward a classification of semidegenerate 3D superintegrable systems ⋮ Bôcher and abstract contractions of 2nd order quadratic algebras ⋮ (Quasi)-exact-solvability on the sphere Sn ⋮ Dynamical symmetry algebras of two superintegrable two-dimensional systems ⋮ Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras

Cites Work

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