Lie Groups and Lie Algebras I
Covers fundamentals of the theory of Lie algebras and related groups. Topics may include theorems of Engel and Lie; enveloping algebra, Poincare-Birkhoff-Witt theorem; classification and construction of semisimple Lie algebras; the center of their enveloping algebras; elements of representation theory; compact Lie groups and/or finite Chevalley groups.
Fall 2020
This course is the first half of the year-long introductory graduate sequence 18.745/18.755 on Lie groups and Lie algebras. Topics include foundations of the theory of Lie groups and Lie algebras; theorems of Engel and Lie; the universal enveloping algebra, the Poincare-Birkhoff-Witt theorem; free Lie algebras; the Campbell-Hausdorff formula; classification and structure of finite dimensional complex simple Lie algebras; their finite dimensional representations; and the Weyl character formula.
Prerequisites & course information
Prereq: ( 18.701 or 18.703 ) and ( 18.100A , 18.100B , 18.100P , or 18.100Q ) G (Fall) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2020
- MIT OCW syllabus ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.