2023
DOI: 10.1088/1751-8121/acb576
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Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras

Abstract: Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial symmetry algebra is proposed. The case of the special linear Lie algebra sl(n) is discussed in detail, where an explicit basis for the commutant with respect to the Cartan subalgebra is obtained, and the order of the polynomial algebra is computed. It is further shown that, with … Show more

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Cited by 4 publications
(3 citation statements)
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“…We briefly review the construction introduced in [26] in regard of commutants, i.e., centralizers of a subalgebra of a Lie algebra in their enveloping algebra and their Poisson-Lie analogue related to the symmetric algebra. Explicitly, we define Definition 1.…”
Section: The Algebraic Setting In the Lie And Poisson-lie Contextmentioning
confidence: 99%
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“…We briefly review the construction introduced in [26] in regard of commutants, i.e., centralizers of a subalgebra of a Lie algebra in their enveloping algebra and their Poisson-Lie analogue related to the symmetric algebra. Explicitly, we define Definition 1.…”
Section: The Algebraic Setting In the Lie And Poisson-lie Contextmentioning
confidence: 99%
“…More details on it can be found e.g. in [25,26]. In the case of sl(n) and other semisimple or reductive algebras, the commutant C U(s) (a) is in fact Noetherian and finitely generated.…”
Section: The Algebraic Setting In the Lie And Poisson-lie Contextmentioning
confidence: 99%
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