E8 roots

Lie Groups and Lie Algebras — 1st Semester 2012/2013




Lecturer: José Natário
Email: jnatar@math.ist.utl.pt
Office: Mathematics Building, 4th floor, room 4.29
Classes: Thursdays from 12:00 to 14:00.
Office Hours:  TBA.



Announcements

This will be a reading course. I will post here every week what you should read for the following week's class. Here "reading" means also trying to solve some exercises.

For the first class (September 27) you should read Appendices A and B. If you are a Mathematics student then you should also read Appendices C and E (just E.1, E.2, E.3 and E.5). However, this material will not be in the tests.

For the second class (October 4) you should read Chapter 1. You can recall the proof of the existence and uniqueness of the Jordan canonical form here (by Edward Nelson).

For the third class (October 11) you should read Chapter 2.

For the fourth class (October 18) you should read Chapter 3.

For the fifth class (October 25) you should read Chapter 4. You can also read Appendix D (but this material will not be in the tests).

For the sixth class (November 8) you should read Chapter 5.

For the seventh class (November 22) you should read Chapter 6.

For the eigth class (November 29) you should read the first half of Chapter 7 (Sections 7.1, 7.2 and 7.3).

For the ninth class (December 6) you should read the second half of Chapter 7 (Sections 7.4, 7.5 and 7.6). You can also read Section E.4 in Appendix E (but this material will not be in the tests).

For the tenth class (December 13) you should read Chapter 8.




Syllabus

General Theory: Matrix Lie Groups, Lie Algebras and the Exponential Mapping, Baker-Campbell-Hausdorff Formula, Basic Representation Theory.

Semisimple Theory: Representations of SU(3), Semisimple Lie Algebras, Representations of Complex Semisimple Lie Algebras, More on Roots and Weights.




Bibliography

Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction




Grading Policy

There will be two tests, each counting 50% towards the grade (dates to be arranged). You will be able to make up for one of these tests the week after classes end.




Tests



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