000			02434 a2200277 4500
001			TB12849
003			IN-BhIIT
005			20260527175143.0
008			260508b |||||||| |||| 00| 0 eng d
020			_a9780387901909 (hbk. )
040			_aIN-BhIIT
041			_aeng
082			_a512.23 _bSER/L
100			_aSerre, J.P. _eAuthor _927773
245			_aLinear representations of finite groups / _cJ.P. Serre and translated by Leonard L. Scott
260			_aNew York : _bSpringer, _c1977.
300			_ax, 170 p. : _bill. ; _c22 cm.
490			_aGraduate texts in mathematics; 42
504			_aIncludes bibliographical references and index.
520			_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.
650			_aMathematics
650			_aModules (Algebra) _xFinite groups _927845
650			_aMathieu groups _xFinite groups _927846
700			_aScott, Leonard L. _eTranslator _927774
942			_cTB
999			_c15498 _d15498