ISU MATH 620X Spring 2020
Lie algebras and their representations
Lectures: MWF 3-4 in Carver 282
Instructor: Dr. Hartwig
Spivak Ch 5.1-5.2
Main text: Kirillov, Jr., An introduction to Lie Groups and Lie Algebras
Week 1: Manifolds, Lie groups, connectedness, G/G^o is discrete
Week 2: Simple connectedness, universal cover of connected manifolds and Lie groups
Week 3: Vector fields, left invariant vector fields, classical groups
Week 4: Immersions and embeddings. Closed Lie subgroups.
Week 8: Representations of sl(2,C). Assignment 2: Casimir operator, Universal enveloping algebra.