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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Kosmann-Schwarzbach, Y. Lie Bialgebras, Poisson Lie Groups, and Dressing Transformations. In: Kosmann-Schwarzbach, Y., Tamizhmani, K.M., Grammaticos, B. (eds) Integrability of Nonlinear Systems. Lecture Notes in Physics, vol 638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40962-5_5
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DOI: https://doi.org/10.1007/978-3-540-40962-5_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20630-9
Online ISBN: 978-3-540-40962-5
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