02434 a2200277 4500 TB12849 IN-BhIIT 20260527175143.0 260508b |||||||| |||| 00| 0 eng d 9780387901909 (hbk. ) IN-BhIIT eng 512.23 SER/L Serre, J.P. Author 27773 Linear representations of finite groups / J.P. Serre and translated by Leonard L. Scott New York : Springer, 1977. x, 170 p. : ill. ; 22 cm. Graduate texts in mathematics; 42 Includes bibliographical references and index. 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. Mathematics Modules (Algebra) Finite groups 27845 Mathieu groups Finite groups 27846 Scott, Leonard L. Translator 27774 TB 15498 15498 0 0 ddc 0 0 SBS CLIITBBS CLIITBBS 2026-03-23 52 4312.26 0 512.23 SER/L TB12849 2026-03-23 00:00:00 5907.20 2026-03-23 TB