By quantum matrix algebras I mean these related to braidings (solutions to Quantum Yang-Baxter Equation) and in a sense similar to the classical matrix algebras. In first turn, I am interested in the so-called Reflection Equation algebra. By using it, me (in collaboration with P.Saponov) have introduced the notion of partial derivatives on the enveloping algebra U(gl(m)). This leads to a new type of Noncommutative Geometry (we call it Quantum Geometry), which is deformation of the classical one. In my talk I plan to consider a way of defining some dynamical models on U(u(2)) background.
