Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras

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Campoamor Stursberg, Otto Ruttwig and Marquette, Ian (2022) Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras. Annals of physics, 437 . ISSN 0003-4916

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Official URL: https://doi.org/10.1016/j.aop.2021.168694



Abstract

We discuss a procedure to determine finite sets M within the commutant of an algebraic Hamiltonian in the enveloping algebra of a Lie algebra g such that their generators define a quadratic algebra. Although independent from any realization of Lie algebras by differential operators, the method is partially based on an analytical approach, and uses the coadjoint representation of the Lie algebra g. The procedure, valid for non-semisimple algebras, is tested for the centrally extended Schrödinger algebras Ŝ(n) for various different choices of algebraic Hamiltonian. For the so-called extended Cartan solvable case, it is shown how the existence of minimal quadratic algebras can be inferred without explicitly manipulating the enveloping algebra.


Item Type:Article
Uncontrolled Keywords:Quadratic algebras; Superintegrable systems; Racah algebras; Conserved quantities; Quantum Hamiltonian
Subjects:Sciences > Mathematics > Algebra
ID Code:73972
Deposited On:07 Sep 2022 11:16
Last Modified:07 Sep 2022 13:56

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