2024/2025

Infinite-Dimensional Lie Algebras

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Filipp Uvarov

Language: English

ECTS credits: 3

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.