Lie algebras on hyperelliptic curves and finite-dimensional integrable systems

2000/10/02 by T. Skrypnyk, Skrypnyk, T.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0010005

Talk given on the XXIII International Colloquium on Group Theoretical Methods in Physics held in Dubna, Russia, 31 July - 5 August,2000

arxiv created 2000/10/02 · openalex publication_date 2000/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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