Description: Linear Representations of Finite Groups by Jean-Pierre Serre, Leonhard L. Scott 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New 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 IEcoie 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. Notes 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. The second part is a course given in 1966 to second-year students of lEcole Normale. The third part is an introduction to Brauer Theory. Table of Contents I Representations and Characters.- 1 Generalities on linear representations.- 2 Character theory.- 3 Subgroups, products, induced representations.- 4 Compact groups.- 5 Examples.- Bibliography: Part I.- II Representations in Characteristic Zero.- 6 The group algebra.- 7 Induced representations; Mackeys criterion.- 8 Examples of induced representations.- 9 Artins theorem.- 10 A theorem of Brauer.- 11 Applications of Brauers theorem.- 12 Rationality questions.- 13 Rationality questions: examples.- Bibliography: Part II.- III Introduction to Brauer Theory.- 14 The groups RK(G), Rk(G), and Pk(G).- 15 The cde triangle.- 16 Theorems.- 17 Proofs.- 18 Modular characters.- 19 Application to Artin representations.- Index of notation.- Index of terminology. Review From the reviews:"Serres book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society) Promotional Corrected fifth printing Long 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 Review Text From the reviews: "Serreas book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society) Review Quote From the reviews:"Serres book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society) Description for Sales People 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. The second part is a course given in 1966 to second-year students of lEcole Normale. The third part is an introduction to Brauer Theory. Details ISBN0387901906 Author Leonhard L. Scott Short Title LINEAR REPRESENTATIONS OF FINI Language English ISBN-10 0387901906 ISBN-13 9780387901909 Media Book Format Hardcover Series Number 0042 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Pages 172 Translator Leonhard L. Scott DOI 10.1007/b25159;10.1007/978-1-4684-9458-7 AU Release Date 1996-10-30 NZ Release Date 1996-10-30 UK Release Date 1996-10-30 Illustrations X, 172 p. Publisher Springer-Verlag New York Inc. Edition Description 1st ed. 1977. Corr. 5th printing 1996 Series Graduate Texts in Mathematics Edition 1st Alternative 9781468494600 DEWEY 510 Audience General Year 1977 Publication Date 1977-09-01 US Release Date 1977-09-01 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96254038;
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ISBN-13: 9780387901909
Book Title: Linear Representations of Finite Groups
Number of Pages: 172 Pages
Language: English
Publication Name: Linear Representations of Finite Groups
Publisher: Springer-Verlag New York Inc.
Publication Year: 1996
Subject: Mathematics
Item Height: 234 mm
Item Weight: 980 g
Type: Textbook
Author: Jean-Pierre Serre
Item Width: 156 mm
Format: Hardcover
