(U. of Saskatchewan/ U. of Virginia)
Abstract: Starting with the finite dimensional simple Lie algebras over the complex numbers, the historical background leading to the discovery of the Kac-Moody Lie algebras will be discussed. The most important of the Kac-Moody algebras are the affine Lie algebras and their classification, structural properties, and their many and varied applications will be indicated. We will see how these developments led to the advent of the extended affine Lie algebras (EALA's) and by using particular examples, indicate how they can be understood and classified. Most of this talk should be accessible to a general mathematical audience including graduate students.