An Introduction to Kac–Moody Groups over Fields

The interest in Kac Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it the need for an introductory textbook on the topic. The aim of this book is twofold: (1) to offer an accessible, reader-friendly, and self-contained introduction to Kac Moody algebras and groups; and (2) to clean the foundations and provide a unified treatment of the theory. The book starts with an outline of the classical Lie theory, used to set the scene. Part II provides a self-contained introduction to Kac Moody algebras. The heart of the book is Part III, which develops an intuitive approach to the construction and fundamental properties of Kac Moody groups. It is complemented by two appendices that offer introductions to affine group schemes and to the theory of buildings. Many exercises are included. The book assumes only a minimal background in linear algebra and basic topology and is addressed to anyone interested in learning about Kac Moody algebras and/or groups, from graduate (master) students to specialists.