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arXiv · 2007.03925

Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems

Rutwig Campoamor-Stursberg·Ian Marquette
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Abstract

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By construction, these algebras do not depend on the choice of realizations by vector fields of the underlying Lie algebra, allowing to propose a procedure to analyze polynomial algebras as those subspaces in an enveloping algebra that commute with a given algebraic Hamiltonian.

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BibTeXRIS

Rutwig Campoamor-Stursberg, Ian Marquette. 2020-08-14. Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems. https://doi.org/10.1016/j.aop.2020.168378

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