Geometric Constructions of Toda and Periodic Toda Chains |
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Authors: | GUO Maozheng LIU Xufeng QIAN Min WAN Bailing |
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Affiliation: | Department of Mathematics, Peking University, Beijing 100871, China |
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Abstract: | A geometrical and neat framework is established to derive both Toda and periodic Toda systems from the geodesics of symmetric spaces. The counterpart of the Iwasawa decomposition of a semisimple Cie group in the case of a loop group is also derived. By these, we get a Lie su balgebra with Lie bracket [,]R, and the corresponding Poisson bracket {,}R gives the Hamiltonian form of the periodic Toda chains. |
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