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Regular version of the site

Article

On Lie groups, cluster variables and integrable systems

International Journal of Modern Physics A. 2013. Vol. 28. No. 3-4. P. 1340007.

We propose an explicit construction for the integrable models on Poisson submanifolds of the Lie groups. The integrals of motion are computed in cluster variables via the Lax map. This generalized construction for the co-extended loop groups allows to formulate, in general terms, some new classes of integrable models.