Course Identification

Title:

Topics in Lie Algebras

Code:

20234162

Lecturers and Teaching Assistants

Lecturers:

Prof. Maria Gorelik

TA's:

N/A

Course Schedule and Location

Year:

2023

Semester:

Second Semester

When / Where:

Thursday, 13:30 - 17:00, Ziskind, Rm 1

First Lecture:

20/04/2023

End date:

21/07/2023

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Lecture; Elective; Regular; 4.00 points

Comments

N/A

Prerequisites

Linear algebra

Introduction to Lie algebras

Restrictions

Participants:

15

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Pass / Fail

Grade Breakdown (in %)

Assignments:

30%

Final:

70%

Evaluation Type

Examination

Scheduled date 1

Date / due date

17/08/2023

Location

Ziskind, Rm 1

Time

0900-1400

Remarks

N/A

Scheduled date 2

Date / due date

20/08/2023

Location

Ziskind, Rm 1

Time

0900-1400

Remarks

N/A

Estimated Weekly Independent Workload (in hours)

5

Syllabus

A construction of Kac-Moody algebras.
Examples.

3. Root systems and Weyl groups.

4. Category O and integrable representations of Kac-Moody algebras.

5. Superalgebras

6. Kac-Moody superalgebras.

7. Classification of Kac-Moody superalgebras.

8. Category O and integrable representations of Kac-Moody superalgebras.

Learning Outcomes

Upon successful completion of this course students should be able to demonstrate understanding of the main concepts of structure theory of Kac-Moody Lie superalgebras and their representations.

Reading List

Victor Kac, Infinite-dimensional Lie algebras.

V. Serganova, Kac-Moody superalgebras and integrability, in

Developments and trends in infinite-dimensional Lie theory, 169--218.

Website

N/A