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We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system.
Sklyanin E. K., On some algebraic structures related to the Yang Baxter equation
1982
Earlier work this paper cites.
Sklyanin E. K., On some algebraic structures related to the Yang Baxter equation. II. Representations of a quantum algebra,
1983
Earlier work this paper cites.
Lee Y.-H.,Links J. and Zhang Y.-Z., Exact solutions for a family of spin-boson systems,
1986
Earlier work this paper cites.
Zhedanov A. S., Hidden Symmetry of Askey-Wilson Polynomials,
1991
Earlier work this paper cites.
Granovsky Ya.A, Zhedanov A.S. and Lutzenko I.M., Quadratic algebra as a ”hidden” symmetry of the Hartmann potential,
1991
Earlier work this paper cites.
Daskaloyannis C, Generalized deformed oscillator and nonlinear algebras
1991
Earlier work this paper cites.
Granovskii Ya.I., Zhedanov A.S. and Lutzenko I.M., Quadratic algebras and dynamics in curved spaces. II. The Kepler problem
1992
Earlier work this paper cites.
Granovskii Ya.I., Lutzenko I.M., Zhedanov A.S., Mutual integrability, quadratic algebras, and dynamical symmetry,
1992
Earlier work this paper cites.
Granovskii Ya.I., Zhedanov A.S., Lutsenko I.M., Quadratic algebras and dynamics in curved space. I. Oscillator,
1992
Earlier work this paper cites.
Zhedanov A.S., Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials,
1993
Earlier work this paper cites.
Bonatsos D., Daskaloyannis C. and Kokkotas K., Quantum-algebraic description of quantum superintegrable systems in two dimensions,
1993
Earlier work this paper cites.
Bonatsos D., Daskaloyannis C. and Kokkotas K., Deformed oscillator algebras for two-dimensional quantum superintegrable systems,
1994
Earlier work this paper cites.
Quesne C., Generalized deformed parafermions, nonlinear deformations of so(3) and exactly solvable potentials,
1994
Earlier work this paper cites.
Létourneau P. and Vinet L., Superintegrable systems: polynomial algebras and quasi-exactly solvable Hamiltonians,
1995
Earlier work this paper cites.
Lavrenov A.N., Deformation of the Askey-Wilson algebra with three generators,
1995
Cited alongside, same era.
Bonatsos D., Daskaloyannis C., Quantum groups and their applications in nuclear physics,
1999
Cited alongside, same era.
Kalnins E.G., Miller W. Jr and Pogosyan G.S.,Superintegrability in three dimensional Euclidean space
1999
Cited alongside, same era.
Daskaloyannis C., Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems,
2001
Cited alongside, same era.
Kalnins E. G., Kress J. M. and Miller W. Jr.,Second order superintegrable systems in conformally flat spaces. 1. 2D classical structure theory,
2005
Cited alongside, same era.
Marquette I., Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials,
2009
Later among the works it cites.
Marquette I., Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics II: Painlevé transcendent potentials,
2009
Later among the works it cites.
Daskaloyannis C., Tanoudis Y., Ternary Poisson algebra for the nondegenerate three dimensional Kepler-Coulomb potential, in Proceedings of the Fourth International Workshop on Group Analysis of Differential Equations and Integrable Systems (October 26-30, 2008, Protaras, Cyprus), University of Cyprus, Nicosia, 2009, 173-181
2009
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Marquette I., Superintegrability and higher order polynomial algebras,
2010
Later among the works it cites.
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Kalnins E. G., Kress J. M. Miller W. Jr., Second order superintegrable systems in conformally flat spaces. 3. 3D classical structure theory,
2005
Cited alongside, same era.
Daskaloyannis C., Ypsilantis K., Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold,
2006
Cited alongside, same era.
Kress J.M., Equivalence of superintegrable systems in two dimensions,
2007
Cited alongside, same era.
Daskaloyannis C., Tanoudis Y., Quantum superintegrable systems with quadratic integrals on a two dimensional manifold,
2007
Cited alongside, same era.
Quesne C., Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions
2007
Cited alongside, same era.
Marquette I. and Winternitz P., Polynomial Poisson algebras for superintegrable systems with a third order integral of motion,
2007
Cited alongside, same era.
Daskaloyannis C. and Tanoudis Y., Classification of the quantum two-dimensional superintegrable systems with quadratic integrals and the Stäckel transforms,
2008
Cited alongside, same era.
2010
Later among the works it cites.
Marquette I, Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras
2010
Later among the works it cites.
Lee Y.-H., Yang W.-L. and Zhang Y.-Z., Polynomial algebras and exact solutions of general quantum nonlinear optical models I: two-mode boson systems,
2010
Later among the works it cites.
Lee Y.-H., Yang W.-L. and Zhang Y.-Z., Polynomial algebras and exact solutions of general quantum nonlinear optical models: II. Multi-mode boson systems,
2010
Later among the works it cites.
Post S., Models of Quadratic Algebras Generated by Superintegrable Systems in 2D,
2011
Later among the works it cites.
Marquette I., An infinite family of superintegrable systems from higher order ladder operators and supersymmetry, Proceeding of the GROUP28: The XXVIII International Colloquium on Group-Theoretical Methods in Physics,
2011
Later among the works it cites.
Kalnins E.G., Kress J.M. and Miller Jr W., A Recurrence Relation Approach to Higher Order Quantum Superintegrability,
2011
Later among the works it cites.
Terwilliger P., The Universal Askey-Wilson Algebra
2011
Later among the works it cites.
Marquette I., Generalized five-dimensional Kepler system, Yang-Coulomb monopole and Hurwitz transformation
2012
Later among the works it cites.
Marquette I. and Quesne C., New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials,
2013
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