Lie Groups and Lie Algebras: Chapters 4-6 (Elements of Mathematics)

Book Details

• Publisher: Springer

• Author: N. Bourbaki

• Language: English

• Edition: 2002

• ISBN: 9783540691716

• Pages: 312

• Cover: Paperback

• Dimensions: 9.2 x 6.1 x 0.7 inches

About The Book

Groups and Reflection by N. Bourbaki is a sophisticated and elegant volume that explores the deep mathematical structures of reflection groups. While it is formally part of the broader Lie group series, this particular volume stands apart as a self-contained and independent treatment, making it accessible to a wide range of mathematicians beyond those specializing in Lie theory.

This book delves into the theory of Coxeter groups, root systems, and the geometry of regular polytopes, forming a rich framework that connects to multiple areas of modern mathematics. Of particular interest are its applications to finite simple groups with a (B, N)-pair structure—also known as Tits systems—and problems related to paving and symmetry in geometry.

Acclaimed by reviewers, including G.B. Seligman, the volume is praised for its clarity, historical insights, and elegant presentation. It is considered both highly accessible and enjoyable for a broad audience, from advanced students to seasoned researchers in fields such as algebra, geometry, group theory, and combinatorics.

This Springer edition preserves the intellectual rigor and depth characteristic of Bourbaki’s works, making it an essential addition to any mathematical library.