Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 10, Tome 172 (1989), pp. 88-98
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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/
@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},
year = {1989},
volume = {172},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a6/}
}
TY - JOUR
AU - V. B. Kuznetsov
AU - A. V. Tsiganov
TI - Infinite series of Lie algebras and boundary conditions for integrable systems
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1989
SP - 88
EP - 98
VL - 172
UR - http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a6/
LA - ru
ID - ZNSL_1989_172_a6
ER -
%0 Journal Article
%A V. B. Kuznetsov
%A A. V. Tsiganov
%T Infinite series of Lie algebras and boundary conditions for integrable systems
%J Zapiski Nauchnykh Seminarov POMI
%D 1989
%P 88-98
%V 172
%U http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a6/
%G ru
%F ZNSL_1989_172_a6
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.
