The coalgebra symmetry method, developed by [Ballestreros et al, 1996] is one of the most fruitful techniques to produce systematically an N-dimensional Hamiltonian integrable system from a 1-dimensional system. This method has been recently adapted for discrete-time systems [Gubbiotti et al, 2023]. In this talk, I will review the methodology itself and share our recent developments concerning the application of formalism to the two-photon Lie algebra h₆. In particular, we give necessary and sufficient conditions for a system of difference equations in quasi-standard form to admit a coalgebra symmetry with respect to the two-photon Lie algebra. Some integrable examples are discussed within this framework.

https://indico.math.cnrs.fr/event/11727/