Math 261a
Textbook: Kirillov Jr. 'An Introduction to Lie Groups and Lie Algebras' + Fulton and Harris ' Representation Theory'.
Class Notes: Here
Location: Dwinelle 130
Time: TTH 9:30-11:00am
Office Hours: By appointment. I'm around, just email me!
HOMEWORK 1: (from Kirillov)
Turn in only those in bold, the rest are just strongly recommended.
Chapter 2: 2.1, 2.4, 2.5,2.8, 2.9, 2.10, 2.15
Chapter 3: 3.1, 3.3, 3.5, 3.6, 3.7 (the nontrivial way), 3.9, 3.10, 3.13, 3.14, 3.16, 3.17, 3.18.
Extra Problems:
1) Show that special (pseudo)orthogonal groups are index 2 subgroups of the (pseudo)orthogonal groups.
2) Finish proving the properties of the exponential map, find the associated lie algebras, and find the dimensions of all the remaining classical Lie groups that we listed but did not do in class.
3) i)Classify complex Lie algebras of dimension at most 3, up to isomorphism.
ii) Classify real Lie algebras of dimension at most 3.
iii) Classify connected complex and real Lie groups of dimension at most 3.