Geodesic
Infinite series of Lie algebras and boundary conditions for integrable systems
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 10, Tome 172 (1989), pp. 88-98

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We construct and study some new representations of the quadratic $R$-matrix algebras in classical and in quantum mechanics which are related to the Toda lattices associated with the classical simple Lie algebras. A new Lax representation for the Manakov top is presented. A dynamical $SO(2,1)$ algebra suited for the study of the adjoint Mathieu functions is constructed. 
@article{ZNSL_1989_172_a6,
     author = {V. B. Kuznetsov and A. V. Tsiganov},
     title = {Infinite series of {Lie} algebras and boundary conditions for integrable systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--98},
     publisher = {mathdoc},
     volume = {172},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a6/}
}
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V. B. Kuznetsov; A. V. Tsiganov. Infinite series of Lie algebras and boundary conditions for integrable systems. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 10, Tome 172 (1989), pp. 88-98. http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a6/