Quantum matrix algebras and their applications

By a quantum matrix algebra (QMA) I mean an algebra generated by entries of a matrix subject to some relations. The best known QMAs are RTT algebras and Reflection Equation ones. Each of them is associated with an R-matrix (constant or depending on parameters). QMAs play a very important role in quantum integrable system theory. I plan exhibit some properties of the mentioned algebras and explain their role in this theory.