Introduction to Lie Algebras

Finite and Infinite Dimension

J. I. Hall

$347

Hardback

Forthcoming
Pre-Order now

QTY:

English

American Mathematical Society
28 February 2025

Algebra; Algebraic geometry

Series: Graduate Studies in Mathematics

Being both a beautiful theory and a valuable tool, Lie algebras form a very important area of mathematics. This modern introduction targets entry-level graduate students. It might also be of interest to those wanting to refresh their knowledge of the area and be introduced to newer material. Infinite-dimensional algebras are treated extensively along with the finite-dimensional ones.

After some motivation, the text gives a detailed and concise treatment of the Killing-Cartan classification of finite-dimensional semisimple algebras over algebraically closed fields of characteristic 0. Important constructions such as Chevalley bases follow. The second half of the book serves as a broad introduction to algebras of arbitrary dimension, including Kac-Moody (KM), loop, and affine KM algebras. Finite-dimensional semisimple algebras are viewed as KM algebras of finite dimension, their representation and character theory developed in terms of integrable representations. The text also covers triangular decomposition (after Moody and Pianzola) and the BGG category $\mathcal{O}$. A lengthy chapter discusses the Virasoro algebra and its representations. Several applications to physics are touched on via differential equations, Lie groups, superalgebras, and vertex operator algebras. Each chapter concludes with a problem section and a section on context and history. There is an extensive bibliography, and appendices present some algebraic results used in the book.

By: J. I. Hall
Imprint: American Mathematical Society
Country of Publication: United States
Volume: 248
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470474997
ISBN 10: 1470474999
Series: Graduate Studies in Mathematics
Pages: 514
Publication Date: 28 February 2025
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

J. I. Hall, Michigan State University, East Lansing, MI