One some algebraic formulations within enveloping algebras related to superintegrability



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Campoamor-Stursberg, Otto Ruttwig (2022) One some algebraic formulations within enveloping algebras related to superintegrability. Analytic and Algebraic Methods in Physics, 62 (1). ISSN 1805–2363

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We report on some recent purely algebraic approaches to superintegrable systems from the perspective of subspaces of commuting polynomials in the enveloping algebras of Lie algebras that generate quadratic (and eventually higher-order) algebras. In this context, two algebraic formulations are possible; a first one strongly dependent on representation theory, as well as a second formal approach that focuses on the explicit construction within commutants of algebraic integrals for appropriate algebraic Hamiltonians defined in terms of suitable subalgebras. The potential use in this context of the notion of virtual copies of Lie algebras is briefly commented.

Item Type:Article
Uncontrolled Keywords:Enveloping algebras, Commutants, Quadratic algebras, Superintegrability
Subjects:Sciences > Mathematics > Algebra
ID Code:74932
Deposited On:04 Oct 2022 12:26
Last Modified:02 Mar 2023 08:59

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