Synopsis
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.
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Language Notes
Text: English (translation)
Original Language: French
Review
From the reviews:
"Serre’s book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society)
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Linear Representations of Finite Groups
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Linear Representations of Finite Groups
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Soft cover. Condition: New. Dust Jacket Condition: New. International Edition. **INTERNATIONAL EDITION** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. Great professional textbook selling experience and expedite shipping service. Seller Inventory # ABE-8054260889
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Linear Representations of Finite Groups (Graduate Texts in Mathematics, 42)
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Linear Representations of Finite Groups
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Hardcover. Condition: Very Good+. Very Good+: shows wear to the lower corner tips and with a touch of crimp to the heel of the back-strip; very mild wear to the head of the back-strip; a mild nudge to the upper front corner tip; a former owner's name and a price both in ink at the upper corner of the front free endpaper; the binding is square and secure; the text is clean. Free of creased or dog-eared pages in the text. Free of any underlining, hi-lighting or marginalia or marks in the text. A carefully used copy, structurally sound and tightly bound, showing mild wear and minor, unobtrusive imperfections. Remains bright and clean. NOT a Remainder, Book-Club, or Ex-Library. Large 8vo (9.5 x 6.3x 0.65 inches). Translated from the French by Leonard L. Scott. Language: English. Weight: 17.5 Ounces. Yellow and white Boards with black and yellow titles at the front panel and back-strip. First published in French in 1971. First English Language Edition (1977) ; Third Corrected Printing (1986) . Hardcover: Lacks DJ as issued. 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 characters. This is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics. ; Graduate Texts in Mathematics; Vol. 42; Large 8vo 9" - 10" tall; x, 170 pages First American Edition; 3rd Corrected Printing. Seller Inventory # 59382
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Linear Representations of Finite Groups (Hardcover)
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ISBN 10: 0387901906
ISBN 13: 9780387901909
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Hardcover. Condition: new. Hardcover. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780387901909
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