Jonas Torbjorn Hartwig
Universidade de Gotheborg, Sweden / IME-USP, Brazil
Hopf algebroids and elliptic quantum groups.
Abstract: Quantum groups are certain Hopf algebras which first appeared in the physics literature in the 1980's. Since then a wide range of connections and applications have been found in many areas of mathematics and physics such as knot theory, special functions, representation theory, etc. A central equation in the theory is the Yang-Baxter equation. In the mid-1990's a generalization of this equation was proposed by Felder, the dynamical Yang-Baxter equation, and the question arose what the corresponding "quantum groups" should be. Through the works of Varchenko, Etingof and others, it was soon understood that these objects need to be something more general than a Hopf algebra. In the talk I plan to give some overview of one of the proposed notions, Hopf algebroids, and report on a recent construction of a Hopf algebroid associated to an elliptic solution to the dynamical Yang-Baxter equation.