Lie Groups, Lie Algebras, and Representations

Lie Groups, Lie Algebras, and Representations
Author :
Publisher : Springer
Total Pages : 452
Release :
ISBN-10 : 9783319134673
ISBN-13 : 3319134671
Rating : 4/5 (73 Downloads)

Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian Hall

Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette


Lie Groups, Lie Algebras, and Representations Related Books

Lie Groups, Lie Algebras, and Representations
Language: en
Pages: 452
Authors: Brian Hall
Categories: Mathematics
Type: BOOK - Published: 2015-05-11 - Publisher: Springer

DOWNLOAD EBOOK

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particul
Representation Theory of Lie Groups
Language: en
Pages: 349
Authors: M. F. Atiyah
Categories: Mathematics
Type: BOOK - Published: 1979 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.
Representations of Compact Lie Groups
Language: en
Pages: 323
Authors: T. Bröcker
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional L
Lie Groups, Lie Algebras, and Their Representations
Language: en
Pages: 444
Authors: V.S. Varadarajan
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the
Introduction to Lie Algebras and Representation Theory
Language: en
Pages: 189
Authors: J.E. Humphreys
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on