# Infinite dimensional Lie algebras, spring 2014

# Infinite dimensional Lie algebras, spring 2014

### Lecturer

### Scope

10 sp.

### Type

Advanced studies. The theory of infinite dimensional Lie algebras and Lie groups is a active branch in modern mathematics with links

to integrable systems, combinatorics, and K-theory. It has also important applications in quantum physics: Quantum field theory models

in low dimensions (conformal field theory) and quantum statistical models in surface physics.

The course starts with an introduction to affine Kac-Moody algebras. We discuss also the associated infinite-dimensional Lie groups.

Finally, we study some applications to conformal field theory and K-theory.

### Prerequisites

Either the course on Lie algebras and representation theory, fall semester 2013 (see the lecture notes on the course homepage),

or basics about Lie algebras and Lie groups obtained in other ways, for example through the course FYMM III, fall semester 2012 (see the

lecture notes).

### Lectures

Weeks 3-9 and 11-18, Monday 10-12 in room B322 and Tuesday 10-12 in room B321.

Easter holiday 17.-23.4.

### Exams

Examination by seminar talks and written reports.

### Bibliography

Kac-Moody algebras: Chapter 5 in the lecture notes "Lie algebras and quantum groups"; an extensive treatise in Victor Kac: Infinite-dimensional

Lie algebras, Cambridge University Press (1990). Infinite-dimensional groups: Boris Khesin and Robert Wendt: The geometry of infinite-dimensional groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3, Springer Verlag (2009).

Affine Dynkin diagrams

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