Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)

Book Details

• Author: Brian Hall

• Publisher: Springer

• Language: English

• Edition: Softcover reprint of the original 2nd ed. 2015

• ISBN: 9783319374338

• Pages: 462

• Cover: Paperback

• Dimensions: 9.1 x 6.0 x 1.2 inches

About The Book

Lie Groups, Lie Algebras, and Representations by Brian Hall is a widely acclaimed and accessible textbook that introduces readers to the theory of Lie groups and Lie algebras with a clear, rigorous approach. Unlike many traditional texts that require a strong background in advanced mathematics, this volume is structured to be approachable with just a foundation in linear algebra, making it an ideal choice for graduate students and advanced undergraduates.

The book systematically develops the theory of matrix Lie groups and their associated Lie algebras while maintaining a balance between mathematical rigor and intuitive explanation. Highlights of the book include an elegant treatment of the Baker–Campbell–Hausdorff formula, a unique and streamlined definition of semisimplicity, and an in-depth presentation of sl(3;C) to introduce root systems and the Weyl group.

This second edition features several major additions, including an entirely new section on the structure and representation theory of compact Lie groups, expanded material on finite-dimensional representations, and comprehensive discussions on universal enveloping algebras, complete with a proof of the Poincaré–Birkhoff–Witt theorem and Verma modules. The inclusion of proofs for the Weyl character formula, Weyl dimension formula, and Kostant multiplicity formula make this a valuable reference for those pursuing advanced study or research in theoretical mathematics and physics.

Highly praised for its clarity and depth, this textbook is considered a standard reference in its field and a must-have for anyone looking to master the foundational tools of Lie theory.