摘要: Quantum groups, even though there is no universally accepted definition, is originated from mathematical physics. It is connected with many other, old and new, areas of mathematics. In this short course, we would like to explore some of those connections.
There will be 5-6 lectures, which I hope to cover the following topics:
1. Hopf algebras and U_q(sl_2) as Hopf algebra;
2. U_q(g) and its representations;
3. Canonical basis;
4. Canonical basis and cluster algebras.
Most parts of the lectures are based on two books: Lectures on quantum groups by Jens Carsten Jantzen and Lectures on quantum groups by Pavel Etingof and Olivier Schiffmann.