{"product_id":"9780387901909","title":"Graduate Texts in Mathematics","description":"\u003ch1\u003eGraduate Texts in Mathematics\u003c\/h1\u003e \u003ch2\u003eSerre, Jean-Pierre; Scott, Leonhard L.\u003c\/h2\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 \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1977-09-01\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387901909\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4684-9458-7\u003c\/p\u003e \u003cp\u003eDimensions: 234cm x156cm\u003c\/p\u003e \u003cp\u003ePages: 172\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44499565478028,"sku":"9780387901909","price":67.45,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387901909.jpg?v=1775711760","url":"https:\/\/lateknightbooks.com\/products\/9780387901909","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}