Lie algebras generated by dynamical systems

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.