Topics in Ring and Representation Theory 2015/16.
This is a first introduction to Lie Algebras. The class meets 14:10-15:00 on Mondays and Tuesdays in 5326, JCMB. Workshops takes place every second week starting in Week 2 (so in all even weeks) on Mondays at 9am (!) in 4325C JCMB.
The book is free to download from the above link! It is also cheap to buy a paperback version, and I would strongly recommend you do this, since there will be no printed lecture notes (though photos of the boards from lectures will be made available, see link below). One place you can purchase the book is here.
- The course follows the book Introduction to Lie Algebras by Erdmann and Wildon. You can download the book for free here, provided you are within the university network.
General course information:
Lecture topics schedule, board photos and typos:
- The detailed syllabus of the course can be found here, which is an update on the drps entry.
- The course information sheet (explaining the December exam and course assignments rules) is here.
- The short teaser for the course written for the Course Fare is here
- We will be working through the main topics in the book in a more-or-less linear way, and the final schedule is available here.
- I will post photos of all the boards from lectures here.
- There is an up-to-date list of known typos and errors in the book here.
Workshop Sheets: Workshop 1, Workshop 2, Workshop 3, Workshop 4, Workshop 5.
- The mock exam is here, and the solutions are here.
- The exam guidance is here.
Assignments:. There is a drawer for assignments outside the MathsHub labelled TRRT: it is one of the bottom green drawers.
Assignment 1: Workshop 1, Q5 and one part of Q6. Due Monday Week 3 by 2pm.
Assignment 2: Workshop 2, Q8. Due Monday Week 5 by 2pm.
Assignment 3: Workshop 3, Q6, 7 and 8. Due Monday Week 7 by 2pm.
Assignment 4: Workshop 4, Q1,2,3,4. Due Monday Week 9 by 2pm.
Example Sheets: Sheet 1, Sheet 2, Sheet 3, Sheet 4, Sheet 5, Sheet 6, Sheet 7, Sheet 8.
Solutions: Solutions 1, Solutions 2, Solutions 3, Solutions 4, Solutions 5, Solutions 6, Solutions 7, Solutions 8.
Tues 22nd Sep: all of Sheet 1, especially 1.2, 1.3 and 1.6.
Tues 29th Sep: Sheet 2, especially 2.1, 2.3 and 2.4
Tues 6th Oct: Sheet 3, especially 3.1, 3.2 and 3.6
Tues 13th Oct: Sheet 4, especially 4.1 and 4.4
Tues 20th Oct: Sheet 5, all!
Tues 27th Oct: Sheet 6, especially 6.2, 6.5, 6.6 and 6.7
Tues 3rd Nov: Sheet 7, especially 7.1, 7.2, and 7.4
Additional Reading. The course textbook is quite exhaustive, but there are many other good books on Lie algebras should you wish to consult them. For example:
If you find any other sources that you think it would be useful that other people know about, email me and I will add them here.
- Representations of Lie Algebras
An Introduction Through gln by Anthony Henderson is another great book, and is available (freely) here. Chapters 2 to 6 are a very good alternative source of information for the first part of the course, and also some of the representation theory parts.
- Introduction to Lie algebras and representation theory by James Humphreys is the most famous textbook in the area, and is available at Murray Library. It is written at a higher abstract level though, and contains much more information than this course. The first two chapters (and parts of the third) are useful if you like thinking more abstractly.
- There many freely available pdf lecture notes which are helpful. For example, the first ten chapters of LieAlgebras.pdf covers most of the course.