Principal structures and methods of representation theory
Author(s)
Bibliographic Information
Principal structures and methods of representation theory
（Translations of mathematical monographs, v. 228）
American Mathematical Society, c2006
- Other Title
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Основные структуры и методы теории представлений
Osnovnye struktury i metody teorii predstavleniĭ
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Note
"Originally published in Russian by МЦНМО under the title 'Основные структуры [и методы] теории представлений' c2004"--T.p. verso
Includes bibliographical references (p. 421-423) and index
Description and Table of Contents
Description
The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups, along with some aspects of ring theory and the theory of algebraic groups.The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Lie algebras and Lie groups, Banach algebras, and quantum groups. This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading. Also available from the AMS by this acclaimed author is ""Compact Lie Groups and Their Representations"".
Table of Contents
Introduction: Basic notions General theory: Associative algebras Lie algebras Topological groups Lie groups Special topics: Semisimple Lie algebras Semisimple Lie groups Banach algebras Quantum groups Root systems Banach spaces Convex sets The algebra $\mathrm{B}(H)$ Bibliography Index.
by "Nielsen BookData"