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A History Of Complex Simple Lie Algebras, Avrila Frazier

Electronic Theses and Dissertations

In 1869, prompted by his work in differential equations, Sophus Lie wondered about categorizing what he called “closed systems of commutative transformations,” while around the same time, Wilhelm Killing’s work on non-Euclidean geometry encountered related topics. As mathematicians recognized this as a division of abstract algebra, the area became known as “continuous transformation groups," but we now refer to them as Lie groups.

Patterns and structures emerged from their work, such as describing Lie groups in connection with their associated Lie algebras, which can be categorized in many important ways. In this paper, we focus on Lie algebras over the …