On finite-dimensional Hopf algebras and their representations
Siu-Hung Ng
Louisiana State University
Abstract: Hopf algebras are generalizations of group algebras. However, finite-dimensional Hopf algebras over are not necessarily semisimple and there could be infinitely many isomorphism classes for a given dimension. In these lectures, we will talk about some basic theorems on finite-dimensional Hopf algebras, which include the uniqueness of integrals, Radford formula of the fourth power of antipodes, and the Nichols-Zoeller Theorem. Applications of these theorems on the classification of Hopf algebras of small dimensions and some invariants of the tensor categories of their representations will be discussed.
Lecture notes
Notes by Harshit Yadav
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Problem session
In charge of Henry Tucker
University of California, San Diego