Linear Representations of Finite Groups by Jean-Pierre Serre

Linear Representations of Finite Groups by Jean-Pierre Serre

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.

From the reviews:

"Serre’s 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)

Professor Jean-Pierre Serre ist ein renommierter franzosischer Mathematiker am College de France, Paris.

SKU	Unavailable
ISBN 13	9780387901909
ISBN 10	0387901906
Title	Linear Representations of Finite Groups
Author	Jean Pierre Serre
Series	Graduate Texts In Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer-Verlag New York Inc.
Year published	1977-09-01
Number of pages	172
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.