Infinite-dimensional Lie algebras and affine quantum groups

Prerequisite

You should be familiar with fundamental notions in algebra and representation theory (basic ring theory, associative algebras, Lie algebras and their universal enveloping algebras, highest weight theory of finite-dimensional Lie algebras). This will be a useful background for the whole course. For the second part of the course, it will be good if you have followed a course on Hopf algebras, braided tensor categories and quantum groups (but I will spend a few lectures on recalling this material).

Abstract

Certain infinite-dimensional algebraic structures and their representations appear naturally in theoretical physics as well as purely mathematical contexts. In this course we will consider Lie algebras such as the oscillator and Virasoro algebras as well as loop algebras and affine Kac-Moody Lie algebras. For the latter the universal enveloping algebras have various well-studied notions of q-deformation.

Lecturer Intro.

Dr. Bart Vlaar has joined BIMSA in September 2022 as an Associate Research Fellow. His research interests are in algebra and representation theory and applications in mathematical physics. He obtained a PhD in Mathematics from the University of Glasgow. Previously, he has held postdoctoral positions in Amsterdam, Nottingham, York and Heriot-Watt University. Before coming to BIMSA he visited the Max Planck Institute of Mathematics in Bonn.