  The general class of the graded Lie algebras is defined. These algebras could
be constructed using an arbitrary dynamical systems with discrete time and with
invarinat measure. In this papers we consider the case of the central extension
of Lie algebras which corresponds to the ordinary crossed product (as
associative algebra) - series A. The structure of those Lie algebras is similar
to Kac-Moody algebras, and these are a special case of so called algebras with
continuous root system which were introduced by author with M.Saveliev in
90-th. The central extension open a new possibilty in algebraic theory of
dynamical systems. The simpliest example corresponds to rotation of the circle
(sine-algebra="quantum torus") and to adding of unity the additvie group of the
p-adic integers.
