Reflection Equation Algebra and its applications to Noncommutative Geometry
Résumé
Reflection Equation Algebra (REA) is one of the central objects of Braided Geometry. By Braided Geometry I mean a theory related to a braiding, i.e. a solution to the Quantum Yang-Baxter Equation. I’ll exhibit properties of the REA related to different types of braidings. 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 of dynamical models of Physics can be generalized to this algebra. A very amusing fact is that these models are in a sense discrete.