Lie Theory

3 credits · Undergraduate

Introduction to Lie algebras and Lie groups: linear groups; universal enveloping algebras; Lie's three theorems; classification of semisimple Lie algebras. Additional topics may include: Lie algebra cohomology; representation theory of semisimple Lie groups; Tannaka-Krein duality; Clifford algebras; Bruhat and Shubert decompositions. PREREQUISITES: MATH 3031.03 and MATH 4045.03 EXCLUSIONS: MATH 5057 FORMATS: Lecture