Groups and Characters

Groups and Characters

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Description

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.show more

Product details

  • Paperback | 239 pages
  • 156 x 232 x 18mm | 421.84g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • black & white illustrations
  • 1584880384
  • 9781584880387
  • 1,386,888

Review quote

"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 CHOICEshow more

Table of contents

Introductory Examples Groups and Subgroups Point Groups and Cosets Homomorphisms and Normal Subgroups Isomorphisms and Automorphisms Factor Groups Sylow Subgroups Permutation Groups Matrix Groups Group Representations Regular Representations Irreducible Representations Representations of Abelian Groups Group Characters Orthogonality Relations and Character Tables Reducible Characters The Burnside Counting Theorem Real Characters Induced Representations and Characters The Character Table for S5 Space Groups and Semi-Direct Products Proofs of the Sylow Theorems References Bibliography Index Index of Symbols.show more