| Linear Representations of Finite Groups 1977. Corr. 5th Edition Contributor(s): Serre, Jean-Pierre (Author), Scott, Leonhard L. (Translator) |
|
 |
ISBN: 0387901906 ISBN-13: 9780387901909 Publisher: Springer OUR PRICE: $71.20 Product Type: Hardcover Published: September 1977 Annotation: This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result of constant use in mathematics as well as in quantum chemistry or physics. The examples in this part are chosen from those useful to chemists. The second part is a course given in 1966 to second-year students of l'Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory. Several Applications to the Artin representation are given. |
| Additional Information |
| BISAC Categories: - Mathematics | Finite Mathematics - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| LCCN: 97105409 |
| Series: Graduate Texts in Mathematics Series |
| Physical Information: 0.67" H x 6.34" W x 9.52" (1.10 lbs) 172 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book consists of three parts, rather different in level and purpose: The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and charac- ters. This is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics. I have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra. The examples (Chapter 5) have been chosen from those useful to chemists. The second part is a course given in 1966 to second-year students of I'Ecoie Normale. It completes the first on the following points: (a) degrees of representations and integrality properties of characters (Chapter 6); (b) induced representations, theorems of Artin and Brauer, and applications (Chapters 7-11); (c) rationality questions (Chapters 12 and 13). The methods used are those of linear algebra (in a wider sense than in the first part): group algebras, modules, noncommutative tensor products, semisimple algebras. The third part is an introduction to Brauer theory: passage from characteristic 0 to characteristic p (and conversely). I have freely used the language of abelian categories (projective modules, Grothendieck groups), which is well suited to this sort of question. The principal results are: (a) The fact that the decomposition homomorphism is surjective: all irreducible representations in characteristic p can be lifted "virtually" (i.e., in a suitable Grothendieck group) to characteristic O. |