Geodesic
Lie algebras generated by dynamical systems
Algebra i analiz, Tome 4 (1992) no. 6, pp. 103-113.

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In this paper we define the class of infinite dimensional $\mathbb Z$-graded Lie algebras generated by dynamical systems and show that these algebras are the special case of .Lie algebras with continuum root system. We establish a precise isomorphism between “sinealgebras” and “rotation-Lie-algebras”, and give the other examples. We briefly mention the algebras of the type $(B)(D)$ and $(C)$ for the dynamical system.
Keywords: Lie algebra, root system, dynamic system, rotation algebra, continuous Dyrikin diagram, $B-C-D$-series. 
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     author = {A. M. Vershik},
     title = {Lie algebras generated by dynamical systems},
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     url = {http://geodesic.mathdoc.fr/item/AA_1992_4_6_a4/}
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A. M. Vershik. Lie algebras generated by dynamical systems. Algebra i analiz, Tome 4 (1992) no. 6, pp. 103-113. http://geodesic.mathdoc.fr/item/AA_1992_4_6_a4/