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.
Course Contents
- Representations of 𝔤𝔩(∞). Semi-infinite wedge product. Japanese cocycle.
- Heisenberg and Virasoro algebras, Fock modules.
- Affine Lie algebras as central extensions of loop algebras. The Sugawara construction.
- Generalized Cartan matrices and Kac – Moody Lie algebras.
- Affine Lie algebras as Kac – Moody Lie algebras.
