Math 508A: Complex Semisimple Lie Algebras

Professor Monty McGovern
Winter 2019


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Instructor:
Monty (or William) McGovern
Office: Padelford C-450
Phone: 206-543-1149
Email: mcgovern@math.washington.edu
Office Hours: drop in, or by appointment
Lectures:
Monday, Wednesday & Friday, 10:30 a.m.-11:20 a.m., Padelford Hall C-401
Required Text:

Introduction to Lie Algebras and Representation Theory by James Humphreys (Springer, 1972)

Prerequisites:
to be in the good graces of the instructor
What to Expect:
This is the second course in the Algebraic Structures sequence. I will classify finite-dimensional complex semisimple Lie algebras, also proving some structural results on general Lie algebras along the way. Although one usually first encounters Lie algebras in a manifolds course, the treatment (following the text) will be entirely algebraic. Homework will be collected every other Friday.

             Homework

Due:
Problems:
Jan 18
1.9; 2.1; 3.8,9; 4.3: read sections 1-6, start section 7
Feb 1
4.5; 7.4,6,7; board problem: show that a semisimple Lie algebra is generated as a Lie algebra by two elements: read 7,8, start Chapter III
Feb 15
10.10,13; 11.2; 13.4, board problem: using large tensor powers of the adjoint representation and sl(2) theory, show that any semisimple Lie algebra L admits irreducible representaitons of arbitrarily large dimension: read 10,12,13
Mar 1
14.1,5; 16.6; 17.3: read 17,18,20
Mar 8
read 21,24; OMIT 22,23


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