Books and papers on Hopf algebras and quantum groups.

Papers

Introduction to quantum groups By Podles and Muller.

8 Lectures on quantum groups and q-special functions

General compact quantum groups, a tutorial

Lectures on Hopf algebras. By Hans-Jürgen Schneider. This is a nice introduction to quantum groups.

On Quantum Groups and Their Potential Use in Mathematical Chemistry This paper is mainly about [tex]su_q(2)[/tex]. They discuss the [tex]q[/tex]-analogues of the harmonic oscillator and angular momentum. It is not an introduction to quantum groups, rather, as the title says, an introduction to some possible uses in chemistry. If you want to learn about quantum groups, this is not the paper.

Quantum Groups and Noncommutative Geometry. By B. Pareigis. A very comprehensive set of notes with a strong categorical flavour. Lots of other nice notes here too.

Hopf algebras, from basics to applications to renormalization By Dominique Manchon. An extended version of a series of lectures given at Bogota in december 2002. It consists in a presentation of some aspects of Connes’ and Kreimer’s work on renormalization in the context of general connected Hopf algebras, in particular Birkhoff decomposition and, in the graded case, the scattering-type formula.

Books
Foundations of Quantum Group Theory This is Majid’s introduction to the theory of quantum groups. I’ve read the first few chapters extensively - these are the most general. Majid gives a lucid and interesting introduction to Hopf algebras and quantum groups. I think this is a great book for someone starting out in quantum groups. It does assume some background in Lie theory but then again - if you don’t know any Lie theory maybe you should read some before trying to tackle quantum groups.

Quantum Groups Kassel’s book is quite readable, it includes plenty of material at an introductory level. Lots of interesting category theory in here as well as the fascinating connections to low dimensional topology and statistical mechanics. I’ve found myself going back to Kassel’s book again and again. I use it in conjunction with Majid’s book. Together they provide a great resource on the subject.

A Guide to Quantum Groups by Chari and Pressley. Another great book for the beginner. I found C and P to be less useful than the other two, though I must admit it is comprehensive and complements Majid’s and Kassel’s books.

I own these three books. I consider the money spent on each of them to be well spent.

Quantum Groups and Their Representations (Texts and Monographs in Physics) This book comes highly recommended by my friend Sacha, I haven’t had a look at it yet, but will be looking at it soon.