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Factorization of the current algebra and integrable top-like systems

I. Z. Golubchik·V. V. Sokolov
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Abstract

A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the Taylor series and some complementary subalgebra. In the case of the Lie algebra $so(3)$ our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows us to generate integrable deformations for known integrable models.

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I. Z. Golubchik, V. V. Sokolov. 2004-03-12. Factorization of the current algebra and integrable top-like systems. https://doi.org/10.1023/b%3Atamp.0000043852.90703.0b

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