Algebras with quantum traces and Quantum double

The purpose of my talk is twofold. First, I plan to consider some algebras related to braidings (i.e. solutions to the Quantum Yang-Baxter equation), which admit introducing quantum traces. Also, I plan to discuss non-unimodular Poisson brackets giving rise to algebras with quantum traces. Second, I plan to introduce some doubles of quantum algebras and to get a new differential calculus arising from such quantum doubles. In particular, such a calculus on the enveloping algebras U(gl(n)) and their braided analogs will be introduced.