02358    a2200253   4500001000800000003000900008005001700017008004100034020002600075040001300101041000800114082001800122100002500140245009500165260003300260300003300293490003800326504005100364520156700415650001601982650003701998650003402035700003502069TB12849IN-BhIIT20260527175143.0260508b        |||||||| |||| 00| 0 eng d  a9780387901909 (hbk. )  aIN-BhIIT  aeng  a512.23bSER/L  aSerre, J.P. eAuthor  aLinear representations of finite groups  /cJ.P. Serre and translated by Leonard L. Scott   aNew York :bSpringer,c1977.  ax, 170 p. :bill. ;c22 cm.   aGraduate texts in mathematics; 42  aIncludes bibliographical references and index.  aThis 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.  aMathematics  aModules (Algebra)xFinite groups  aMathieu groupsxFinite groups  aScott, Leonard L. eTranslator