18 745 - Introduction to Lie Algebras

Institution:

Massachusetts Institute of Technology

Subject:

Description:

Structure of finite-dimensional Lie algebras. Theorems of Engel and Lie. Cartan subalgebras and regular elements. Trace form and Cartan's criterion. Chevalley's conjugacy theorem. Classification and construction of semisimple Lie algebras. Weyl group. Universal enveloping algebra and the Casimir operator. Weyl's complete reducibility theorem, Levi and Maltsev theorems. Verma modules. Classification of irreducible finite-dimensional representations of semisimple Lie algebras. Weyl's character and dimension formulas.

Credits:

3.00

Credit Hours:

Prerequisites:

Prereq: 18.701 or 18.703

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

web.mit.edu/student/

Phone Number:

(617) 253-1000

Regional Accreditation:

New England Association of Schools and Colleges

Calendar System:

Four-one-four plan

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