The sl2(R) coalgebra symmetry and the superintegrable discrete-time systems

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.