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Lie algebras on hyperelliptic curves and finite-dimensional integrable systems

T. Skrypnyk
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Abstract

We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two subalgebras. These two facts together enables one to use them to construct new integrable finite-dimensional hamiltonian systems. In such a way we find new integrable hamiltonian systems, which are direct higher rank generalizations of the integrable systems of Steklov-Liapunov, associated with the e(3) algebra and Steklov-Veselov associated with the so(4) algebra.

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T. Skrypnyk. 2000-10-02. Lie algebras on hyperelliptic curves and finite-dimensional integrable systems. https://arxiv.org/abs/nlin/0010005

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