CU Algebraic Lie Theory Seminar

Introduction to universal enveloping algebras

Richard Green, CU

Abstract

The universal enveloping algebra of a Lie algebra is an associative algebra with the same representation theory. This sequence of talks will be a (possibly intermittent) mini-course in Lie algebras and enveloping algebras, using only MATH 6130/6140 as a prerequisite. It is recommended that students take notes. Topics to be covered include Lie algebras, enveloping algebras, Hopf algebras, the Serre presentation, the triangular decomposition, Verma modules, simple modules and quantized enveloping algebras. The talks will focus on Lie theory and representation theory, not universal algebra as the title might imply.