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Integrability of Nonlinear Systems pp 104–170Cite as

Lie bialgebras, poisson Lie groups and dressing transformations

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Part of the book series: Lecture Notes in Physics ((LNP,volume 495))

Abstract

In this course, we present an elementary introduction, including the proofs of the main theorems, to the theory of Lie bialgebras and Poisson Lie groups and its applications to the theory of integrable systems. We discuss r-matrices, the classical and modified Yang-Baxter equations, and the tensor notation. We study the dual and double of Poisson Lie groups, and the infinitesimal and global dressing transformations.

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  1. Centre de Mathématiques, URA 169 au CNRS Ecole Polytechnique, F-91128, Palaiseau, France

    Y. Kosmann-Schwarzbach

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  1. Y. Kosmann-Schwarzbach
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Y. Kosmann-Schwarzbach B. Grammaticos K. M. Tamizhmani

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Kosmann-Schwarzbach, Y. (1997). Lie bialgebras, poisson Lie groups and dressing transformations. In: Kosmann-Schwarzbach, Y., Grammaticos, B., Tamizhmani, K.M. (eds) Integrability of Nonlinear Systems. Lecture Notes in Physics, vol 495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113695

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  • DOI: https://doi.org/10.1007/BFb0113695

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  • Print ISBN: 978-3-540-63353-2

  • Online ISBN: 978-3-540-69521-9

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