{"product_id":"linear-representations-of-finite-groups-graduate-texts-in-mathematics-42-0387901906","title":"Linear Representations of Finite Groups (Graduate Texts in Mathematics, 42)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0387901906\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Serre, Jean-Pierre\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51539053150496,"sku":"NEW0387901906","price":72.22,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/61pr-qSZuSL.jpg?v=1777483897","url":"https:\/\/miakarts.com\/products\/linear-representations-of-finite-groups-graduate-texts-in-mathematics-42-0387901906","provider":"Miakarts Books","version":"1.0","type":"link"}