This Is AuburnElectronic Theses and Dissertations

On the Conjugacy Theorems of Cartan and Borel Subalgebras

Date

2010-04-09

Author

Thompson, Mary Clair

Type of Degree

thesis

Department

Mathematics and Statistics

Abstract

We study the conjugacy theorems of Cartan subalgebras and Borel subalgebras of general Lie algebras. We present a history of the problem, along with two proofs of the theorems which stay completely within the realm of Lie algebras. The first is a reworking by Humphreys of an earlier proof, relying upon the ideas of Borel subalgebras and using double induction. The second proof is a newer proof presented by Michael which substantially simplifies the theory.