| Document Type
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BL
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| Record Number
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599000
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| Doc. No
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b428219
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| Main Entry
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Weintraub, Steven H.
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| Title & Author
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Representation theory of finite groups : : algebra and arithmetic /\ Steven H. Weintraub.
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, ©2003.
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| Series Statement
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Graduate studies in mathematics,; v. 59
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| Page. NO
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ix, 212 pages ;; 26 cm.
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| ISBN
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0821832220
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: 9780821832226
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| Bibliographies/Indexes
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Includes bibliographical references (page 209) and index.
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| Contents
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Ch. 1. Introduction -- Ch. 2. Semisimple Rings and Modules -- 2.1. Basic Notions -- 2.2. Structure Theorems -- 2.3. Idempotents and Blocks -- 2.4. Behavior under Field Extensions -- 2.5. Theorems of Burnside and Frobenius-Schur -- Ch. 3. Semisimple Group Representations -- 3.1. Examples and General Results -- 3.2. Representations of Abelian Groups -- 3.3. Decomposition of the Regular Representation -- 3.4. Applications of Frobenius's Theorem -- 3.5. Characters -- 3.6. Idempotents and their Uses -- 3.7. Subfields of the Complex Numbers -- 3.8. Fields of Positive Characteristic -- Ch. 4. Induced Representations and Applications -- 4.1. Induced Representations -- 4.2. Mackey's Theorem -- 4.3. Permutation Representations -- 4.4. M-groups -- 4.5. Theorems of Artin and Brauer -- 4.6. Degrees of Irreducible Representations -- Ch. 5. Introduction to Modular Representations -- Ch. 6. General Rings and Modules -- 6.1. Jordan-Holder and Krull-Schmidt Theorems -- 6.2. The Jacobson Radical -- 6.3. Rings of Finite Length -- 6.4. Finite-dimensional Algebras -- Ch. 7. Modular Group Representations -- 7.1. General Results -- 7.2. Characters and Brauer Characters -- 7.3. Examples -- App. Some Useful Results.
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| Abstract
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"The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference."--Jacket.
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| Subject
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Representations of groups.
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| Subject
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Finite groups.
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| LC Classification
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QA176.W45 2003
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