Groups and Characters

by Victor E Hill

Overview

Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. This book offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, it emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The text includes sections that provide the mathematical basis for some of the applications of group theory. It also offers numerous exercises, some stressing computation of concrete examples, others stressing development of the theory.

Product Details

ISBN-13:	9781351443807
Publisher:	CRC Press
Publication date:	12/12/2018
Sold by:	Barnes & Noble
Format:	eBook
Pages:	239
File size:	6 MB

About the Author

Victor E Hill

Table of Contents

Preface, 1 Introductory Examples, 2 Groups and Subgroups, 3 Point Groups and Cosets, 4 Homomorphisms and Normal Subgroups, 5 Isomorphisms and Automorphisms, 6 Factor Groups, 7 Sylow Subgroups, 8 Permutation Groups, 9 Matrix Groups, 10 Group Representations, 11 Regular Representations, 12 Irreducible Representations, 13 Representations of Abelian Groups, 14 Group Characters, 15 Orthogonality Relations and Character Tables, 16 Reducible Characters, 17 The Burnside Counting Theorem, 18 Real Characters, 19 Induced Characters, 20 The Character Table for S5, 21 Space Groups and Semidirect Products, 22 Proofs of the Sylow Theorems, Bibliography, Index of Symbols, Index

Editorial Reviews

Hill (mathematics, Williams College, Massachusetts) introduces the theory of group and group characters at an easier level of mathematics than the classic works by Curtis and Reiner. He addresses undergraduate or beginning graduate mathematics students who want to get their feet wet before plunging into the subject; students in chemistry, physics, or geology who might encounter groups and characters is such areas as crystallography or quantum mechanics; and physical scientists whose exposure to the techniques has been less than rigorous and would like to understand the mathematics behind them. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"…rigorous and appropriate…excellent starting point for anyone interested in the theory of groups, representations and characters. Upper division undergraduates through professionals."
-D. S. Larson, Gonzago University in CHOICE

From the Publisher