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.