Braided Geometry and its applications

By Braided Geometry I mean a theory related to a braiding, i.e. a solution to the Quantum Yang-Baxter Equation. One of the central objects of Braided Geometry is Reflection Equation Algebra (REA). I'll exhibit properties of different types of braidings and the corresponding REA. Also, I'll explain the role of the REA in constructing a differential calculus on the enveloping algebra U(gl(n)). In the case $n=2$ this calculus leads to a noncommutative version of the Minkowski space algebra. Many dynamical models can be generalized to this algebra. A very amusing fact is that these models are in a sense discrete.