Loop groups and string topology

TL;DR

This survey explores the theory of loop groups, their central extensions, and positive energy representations, providing an overview of their algebraic and topological properties based on a series of academic lectures.

Contribution

It offers a comprehensive summary of loop groups and their representations, highlighting recent developments and pedagogical insights from a specialized summer school course.

Findings

Overview of loop groups and their properties

Discussion of central extensions and positive energy representations

Summarization of recent research and open problems

Abstract

Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.