Quantum vertex algebras

In 1998 P. Etingof and D. Kazhdan defined the notion of quantum vertex algebra. They started from the definition of vertex algebra and they replaced the underlying vector space with a topologically free K[[h]]-module, then they deformed the locality introducing a braiding map which is a solution of the quantum Yang-Baxter equation. Since the obtained object, called braided vertex algebra, doesn't satisfy the associativity relation they imposed an additional axiom called "Hexagon relation" which implies the associativity relation. In their foundational article, P. Etingof and D. Kazhdan gave also a nontrivial example of quantum vertex algebra: the quantum affine vertex algebra. In the first part of our work we study the notion of S-commutative braided vertex algebras which satisfy the associativity relation, we give a characterization of braided vertex algebras which satisfy the associativity relation and we prove in every detail that the example given by P. Etingof and D. Kazhdan satisfies all the axioms of a quantum vertex algebra. In the second part we deal with Drinfeld's notes on universal triangular R-matrices