Topics in Lie Theory: Tensor Categories
An advanced graduate course from MIT OpenCourseWare on tensor categories and their role in representation theory. The syllabus builds up the theory of tensor categories as a categorification of ring theory, covering analogues of modules, module morphisms, Morita equivalence, commutative rings, the center of a ring, the centralizer of a subring, the double centralizer property, and graded rings. Materials include lecture notes and course readings published under MIT's open license, following the structure of a semester-long topics course rather than a single talk. The course assumes strong background in abstract algebra and representation theory and is aimed at students already comfortable with Lie theory who want to see how categorical language reframes familiar ring-theoretic concepts. No certificate is offered, consistent with MIT OpenCourseWare's model of publishing course materials for independent study.