The $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems

Giorgio Gubbiotti; Danilo Latini

doi:10.1088/1402-4896/acbbb2

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arXiv · 2210.17171

The $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems

Giorgio Gubbiotti·Danilo Latini

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Abstract

In this paper, we classify all the variational discrete-time systems in quasi-standard form in $N$ degrees of freedom admitting coalgebra symmetry with respect to the generic realisation of the Lie-Poisson algebra $\mathfrak{sl}_{2}(\mathbb{R})$. This approach naturally yields several quasi-maximally and maximally superintegrable discrete-time systems, both known and new. We conjecture that this exhausts the (super)integrable cases associated with this algebraic construction.

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Giorgio Gubbiotti, Danilo Latini. 2022-10-31. The $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems. https://doi.org/10.1088/1402-4896%2Facbbb2

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