# An algebraic approach to discrete time integrability

@article{Doikou2020AnAA, title={An algebraic approach to discrete time integrability}, author={Anastasia Doikou and Iain Findlay}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2020}, volume={54} }

We propose the systematic construction of classical and quantum two-dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated r-matrices and underlying spatial and temporal classical and quantum algebras. This is a novel construction that leads to the derivation of fully discrete integrable systems governed by sets of consistent integrable non-linear space-time difference equations. To illustrate the proposed methodology, we derive two…

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