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Easter term revision schedule
Revision Class: Monday, May 27th, 4-5pm in MR5.
Office Hours (in E0.15, or outside Pavilion E if the weather is nice)
Friday, May 3rd, 4-5pm.
Friday, May 17th, 4-5pm.
Thoughts on studying:
Last year’s exam is a pretty good indicator of what this year’s exam will be like.
While studying, spend more time working through example sheet problems and less time trying to memorize your notes.
When taking the exam, you should remember to write in complete sentences (these sentences will contain mathematical symbols/notation, but should be complete thoughts expressed in such a way that I can follow your logic while grading).
Teaching assistants for the course are Jef Laga and Marius Leonhardt.
Course philosophy
Lie algebras play a role in many diverse areas of mathematics, from number theory to theoretical physics. The material in this course is beautiful in its own right, but the main purpose of the course is to gain familiarity with these objects so that you can work with them in the context of your interests. Because of this, we will spend time on examples, and students should expect to actively engage during lectures. Because of the amount of material we will need to cover to give you a solid background, we will sometimes skip or sketch proofs that can be found in the references below. (Note that proofs we don't do in class are non-examinable.)
How to get the most out of this course
Work on the example sheets! Let the problems guide you as you review your notes: you don't have to carefully read every line of the lecture notes before starting an example sheet.
Come to office hours with specific questions about example-sheet problems you're stuck on.
Hand in problems to be marked: this is your only chance to get feedback on your work.
Example Sheets
Sheet 1, problems for marking due October 16th.
Sheet 2, problems for marking due October 31st.
Sheet 3, problems for marking due November 14th.
Sheet 4, problems for marking due January 22nd.
Example Classes (Please go to the class you've signed up for!)
October 17th, 2pm and 3pm, in MR11 and MR15
November 1st, 3pm and 4pm in MR11 and MR13
November 15th, 2pm and 3pm in MR13; 2pm in MR14; 3pm in MR11
January 24th, 2pm and 3pm in MR11 and MR15.
Office Hours (in E0.15)
October 12th, 4-5pm
October 26th, 4-5pm
November 9th, 4-5pm.
November 12th, 4:30-5:30pm, at the Punter, 3 Pound Hill.
November 26th, 4-5pm (in E0.15).
January 21st, 4-5pm (in E0.15).
References
Humphreys, James E. Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, 9, Springer-Verlag New York-Berlin, 1978.
Carter, R. W. Lie algebras of finite and affine type, Cambridge Studies in Advanced Mathematics, 96, Cambridge University Press, Cambridge, 2005.
Fulton, William and Harris, Joe. Representation theory, Graduate Texts in Mathematics, 129, Springer-Verlag, New York, 1991.
Serre, Jean-Pierre. Complex Semisimple Lie Algebras. trans. G.A. Jones. Springer Monographs in Mathematics, Springer-Verlag, New York, 2001.
Carter, Roger W. Simple groups of Lie type, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989.
Kostant, Bertram. The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, American Journal of Mathematics, Vol. 81, No. 4 (Oct., 1959), pp. 973-1032.
Useful links
Notes from a previous version of this course, taught by Ian Grojnowski
Graph paper for rank-two root systems
Spherical explorer for explicit descriptions of root systems
Notes about the representation theory of finite groups by Mark Reeder
For the proof about complete reducibility, see Theorem 2.1 in these notes by Pete L. Clark
Extras on exceptional root systems
Pictures of the E6, E7, and E8 root systems
The Octonions by John Baez
What is G2? by Martin Weissman
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