Having explored some of the representation theory of quantum
sl_2, I will give the definition of the quantum group in general. I
will then discuss R-matrices and the braided monoidal structure. We
will then describe the integral forms of quantum groups, and how this
allows one to consider representation theory at a root of unity. If
time permits I will discuss tilting modules, and how a quotient
construction allows one to construct finite semi-simple braided tensor
categories.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3861