Infinite-Dimensional Lie Algebras

2024/2025

Academic Year

ENG

Instruction in English

3

ECTS credits

Delivered at:

Faculty of Mathematics

Course type:

Optional course (faculty)

When:

3, 4 module

Instructor

Uvarov, Filipp

Course Syllabus

Abstract

Infinite-dimensional Lie algebras naturally arise in quantum field theory and differential geometry (for example, as Lie algebras of vector fields). Unlike in finite-dimensional case, the understanding of infinite-dimensional Lie algebras and their representations is far from being complete. In this course, we will cover the most famous and studied examples of infinite-dimensional Lie algebras, whose structure theory and representations on the one hand, resemble those of finite-dimensional simple Lie algebras, on the other hand, posses new interesting features.