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Features of Discrete Integrability

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Quantum Theory and Symmetries

Part of the book series: CRM Series in Mathematical Physics ((CRM))

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Abstract

We describe some standard features of integrability for a class of integrable partial difference equations: the quad equations. These features are the existence of Lax pairs, higher dimensional consistency, singularity properties, existence of symmetries, and low complexity (vanishing algebraic entropy). All these features have pros and cons, and we give a glimpse of them.

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Acknowledgements

The author would like to thank the organisers of the 11th symposium “Théorie Quantique et Symétries” for the invitation at the Centre de Recherches Mathématiques, in particular at the occasion of the “Special Session in honour of Decio Levi: Integrability: continuous and discrete, classical & quantum.”

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Authors and Affiliations

  1. Centre National de la Recherche Scientifique, Sorbonne Université, Paris, France

    Claude M. Viallet

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  1. Claude M. Viallet
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Correspondence to Claude M. Viallet .

Editor information

Editors and Affiliations

  1. Département de physique, Université de Montréal, Montréal, QC, Canada

    M. B. Paranjape

  2. Département de physique, Université de Montréal, Montréal, QC, Canada

    Richard MacKenzie

  3. Department of Mathematics and Physics, SUNY Polytechnic Institute, Utica, NY, USA

    Zora Thomova

  4. Department of Mathematics and Statistics, Université de Montréal, Montréal, QC, Canada

    Pavel Winternitz

  5. Département de physique, Université de Montréal, Montréal, QC, Canada

    William Witczak-Krempa

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Viallet, C.M. (2021). Features of Discrete Integrability. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_2

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