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Organization, Regulations, and Courses 2022-23

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.



Degree Requirement Attributes


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  • Spring