Course Identification
Introduction to Lie algebras
Lecturers and Teaching Assistants
Prof. Maria Gorelik
Course Schedule and Location
Monday, 09:15 - 11:00, Jacob Ziskind Building, Rm 155
05/11/2018
Field of Study, Course Type and Credit Points
Mathematics and Computer Science: Lecture; Elective; 2.00 points
Comments
Location change- to room 155
On 10/12 the lecture will be held at FGS room C
Prerequisites
A course in Linear Algebra
Attendance and participation
Scheduled date 1
21/02/2019
Jacob Ziskind Building, Rm 155
Scheduled date 2
17/03/2019
Jacob Ziskind Building, Rm 155
Estimated Weekly Independent Workload (in hours)
Syllabus
- Definition of a Lie algebra, examples.
- Representations, representation theory of sl(2)
- Solvable and nilpotent Lie algebras, Engel's Theorem, Lie's Theorem
- Simplicity and semi-simplicity, Killing form, Cartan's criterion
- Complete reducibility of representations, Casimir element
- Root systems, Weyl group
- Cartan matrix, Dynkin diagrams
- Classification of complex semi-simple Lie algebras
- Universal enveloping algebra, Poincare-Birkoff-Witt Theorem
- Verma modules
- Weyl Character formula
Learning Outcomes
Upon successful completion of this course students should be able to:
Demonstrate an understanding of the concepts of structure theory of complex semisimple Lie algebras and their representations.
Reading List
Suggested Reading: J. E. Humphreys "Introduction to Lie Algebras and Representation Theory"