Lie algebras on hyperelliptic curves and finite-dimensional integrable systems

Details Lie algebras on hyperelliptic curves and finite-dimensional integrable systems Lie algebras on hyperelliptic curves and finite-dimensional integrable systems

2000-10-02

arxiv.org/abs/nlin/0010005v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Talk given on the XXIII International Colloquium on Group Theoretical Methods in Physics held in Dubna, Russia, 31 July - 5 Au

Scientific paper

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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