Groups and Characters

Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters.

Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5.

The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory.

Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.

Zusatztext "?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 Informationen zum Autor Victor E Hill Klappentext This text provides an easy to follow introduction to the theory of groups and of group characters. The author presents group theory through the Sylow Theorems and uses many worked-out examples, including the full subgroup structure of A5. Representations and characters are worked out with numerous character tables plus real and induced characters that lead to the table for S5. The book includes sections that provide the mathematical basis for some of the applications of group theory in spectroscopy and molecular structure. It is also full of exercises that five the reader a sense of the applications to larger projects. Zusammenfassung Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Designed as a rapid survey of the subject, this book emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. Inhaltsverzeichnis 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...

"rigorous and appropriateexcellent 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

Autorentext

Victor E Hill

Klappentext

This text provides an easy to follow introduction to the theory of groups and of group characters. The author presents group theory through the Sylow Theorems and uses many worked-out examples, including the full subgroup structure of A5. Representations and characters are worked out with numerous character tables plus real and induced characters that lead to the table for S5. The book includes sections that provide the mathematical basis for some of the applications of group theory in spectroscopy and molecular structure. It is also full of exercises that five the reader a sense of the applications to larger projects.

Inhalt
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