MATH 8300 - Topics in Algebra: Quantum Groups - Spring 2020

| Class Lecture Notes | Homework | Reading |

General Information

Time MWF, 1:25 p.m. -- 2:15 p.m.
Location Vincent Hall, Room 2
Professor Ben Brubaker (
Office: Vincent Hall, Room 352
Office Phone: 612-625-7396
Office Hours: MWF 11:00-12:00, and always available by appointment
Textbook None required, we use a combination of notes prepared by me and small segments of several textbooks (see "Further Reading" below)
3 optional problem sets over the semester,
an optional presentation on a special topic at the end of the course,
no exams (Note: undergraduates enrolled will be required to submit problem sets and do a final presentation)
Course Ad Linked here as a pdf.


There will be 3 problem sets over the course of the semester (roughly one every 4 weeks) posted here.

  • Problem Set 1, due Friday, February 21. (TeX source file)
  • Problem Set 2, due Friday, March 27. (TeX source file)
  • Reading Materials

    As noted above, there is no required textbook. I will post scans of my own course notes on the Class Lecture Notes page, linked above. For the most part, these will be inspired by the following sources:

    • "Quantum Groups" by Christian Kassel (Springer GTM 155)
    • "A Quantum Groups Primer" by Shahn Majid (London Math. Soc. Lecture Note Series 292) - this book has real insight and is nicely divided into individual lectures of reasonable size. Better still, UMN students have online access to the book through the library website.
    • "Lectures on Quantum Groups" by Jens Carsten Jantzen (AMS Graduate Studies, Vol. 6)
    • "A Guide to Quantum Groups" by V. Chari and A. Pressley (Cambridge Univ. Press)
    Many of the above sources assume a familiarity with representation theory and algebraic groups that we won't assume! In particular, throughout the course, we will remind the audience about basic notions in representation theory of algebras. See for example:
      Online notes on quantum groups:

    • Notes on Quantum Groups from a course given by my longtime collaborator Daniel Bump, at Stanford University in 2019. They are written as Beamer slides, and include a number of very nice pictures.