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Read or Download Lie Groups, Lie Algebras, and Rep

Read online or Download Lie Groups, Lie Algebras, and Representations: An Elementary Introduction / Edition 1 (Full PDF ebook with essay, research paper)
by Brian Hall


Product Details

ISBN-13:
9781441923134
Publisher:
Graduate Texts in Mathematics Series, #222
Edition description:
Softcover reprint of hardcover 1st ed. 2003
Pages:
354
Sales rank:
942,338
Product dimensions:
0.78(w) x 9.21(h) x 6.14(d)

Overview

 

Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.

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