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}
}
  • A. DoikouIain Findlay
  • Published 2 September 2020
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
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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