Flow of finite-dimensional algebras

We introduce the notion of flow (depending on time) of finite-dimensional algebras (FA). This flow can be considered as a particular case of (continuous-time) dynamical system whose states are finite-dimensional algebras with matrices of structural constants satisfying an analogue of Kolmogorov-Chapman equation. We define stochastic FA generated by known quadratic stochastic processes and give a construction of an FA which contains algebras of arbitrary (finite) dimension. We discuss the time depending behavior (dynamics) of the properties in FA.