MATH 72.02 Lie Groups: An Introduction Via Matrix Groups
Created by Sophus Lie (1842-1899) with the intent of developing a “Galois theory” of differential equations, Lie groups are a mathematically rigorous realization of our intuitive notion of “continuous transformation groups” and play a fundamental role in the study of geometry and physics.
Formally, a Lie group is a group G equipped with the structure of a smooth manifold with respect to which the group operations (i.e., multiplication and inversion) are smooth. Our exploration of Lie groups will begin with the study of “matrix groups” (e.g., SO(n), SU(n), Sp(n) and SLn(R)). By focusing on this concrete class of examples, we will build our intuition and encounter many of the interesting themes that arise in the general theory of Lie groups.
Prerequisite
MATH 71, or permission of the instructor. Depending on the specific topics covered,
MATH 31 may not be an acceptable prerequisite; however, in consultation with the instructor,
MATH 31 together with some outside reading should be adequate preparation for the course.