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- W2950798088 abstract "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. We obtain the corresponding quartic (associative) algebra for the quantum analog and we extend Daskaloyannis' construction in obtained in context of quadratic algebras and we obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite dimensional unitary irreductible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptionnal orthogonal polynomials introduced recently." @default.
- W2950798088 created "2019-06-27" @default.
- W2950798088 creator A5049413367 @default.
- W2950798088 date "2013-04-26" @default.
- W2950798088 modified "2023-09-27" @default.
- W2950798088 title "Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras" @default.
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