On the Conjugacy Theorems of Cartan and Borel Subalgebras
Type of Degreethesis
Mathematics and Statistics
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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.