A Course on Lie algebras and Chevalley groups

Meinolf Geck

Published 2024-04-17Version 1

These are notes of a graduate course on semisimple Lie algebras and Chevalley groups (over arbitrary fields). The aim is to give a self-contained introduction to these topics based on Lusztig's recent simplified approach, which is inspired by the general theory of ``canonical'' bases. Many constructions are of a purely combinatorial nature and, hence, can be implemented on a computer. We explicitly incorporate such algorithmic methods in our treatment. This is the first part of a planned book project.