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arXiv · 2601.10625

Discrete-time maximally superintegrable systems and deformed symmetry algebras: the Calogero-Moser case

Pavel Drozdov·Giorgio Gubbiotti·Danilo Latini
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Abstract

We determine the complete structure of the symmetry algebras associated with the N-body Calogero-Moser system and its maximally superintegrable discretization. We prove that the discretization naturally leads to a nontrivial deformation of the continuous symmetry algebra, with the discretization parameter playing the r\^ole of a deformation parameter. This phenomenon illustrates how discrete superintegrable systems can be viewed as natural sources of deformed polynomial algebraic structures. As a byproduct of these results, we also reveal a connection between the above-mentioned symmetry algebras and the Bell polynomials, as a consequence of the trace properties.

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Pavel Drozdov, Giorgio Gubbiotti, Danilo Latini. 2026-01-15. Discrete-time maximally superintegrable systems and deformed symmetry algebras: the Calogero-Moser case. https://doi.org/10.1016/j.physd.2026.135323

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