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Poisson Geometry of Difference Lax Operators and Difference Galois Theory

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Operator Theory, Operator Algebras and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 242))

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Abstract

We discuss the lift of Poisson structures associated with auxiliary linear problems for the differential and difference Lax equations to the space of wave functions. Due to a peculiar symmetry breaking, the corresponding differential and difference Galois groups become Poisson Lie Groups.

Mathematics Subject Classification (2010). 37K65; Secondary 12H05 35Q53 37K10.

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Author information

Authors and Affiliations

  1. Institut Mathématique de Bourgogne, 9 avenue A. Savary, F-21078, Dijon, France

    Michael Semenov-Tian-Shansky

  2. Steklov Mathematical Institute, 191023, 27 Fontanka, St. Petersburg, Russia

    Michael Semenov-Tian-Shansky

Authors
  1. Michael Semenov-Tian-Shansky
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Correspondence to Michael Semenov-Tian-Shansky .

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Editors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal

    M. Amélia Bastos

  2. Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal

    Amarino Lebre

  3. Departamento de Matemática, Universidade do Algarve, Faro, Portugal

    Stefan Samko

  4. Department of Mathematics, College of William & Mary, Williamsburg, Virginia, USA

    Ilya M. Spitkovsky

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Semenov-Tian-Shansky, M. (2014). Poisson Geometry of Difference Lax Operators and Difference Galois Theory. In: Bastos, M., Lebre, A., Samko, S., Spitkovsky, I. (eds) Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, vol 242. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0816-3_21

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