Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
42 (2001), S. 4570-4581
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A new family of infinite-dimensional Lie algebras on hyperelliptic curves is constructed. We show them to be quasigraded and explicitly find their central extensions. We also show, that constructed algebras in the case of zero central charge possess infinite number of invariant functions. Besides, they admit a decomposition into the direct sum of two subalgebras. These two facts together enables one to use them to construct new integrable 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. Besides we give hyperelliptic Lax representation for the generalized Euler tops. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1379066
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