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An Introduction to Lie Groups and Lie Algebras

$39.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2017
  • availability: Available
  • format: Paperback
  • isbn: 9781316614105

$ 39.99 (P)
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  • This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.

    • The exposition emphasizes the main concepts rather than technical details of the proofs, making it possible to cover a lot of material in relatively concise work
    • Numerous exercises and worked examples, as well as a sample syllabus, make this an ideal text for a graduate course on Lie groups and Lie algebras
    • Focusses on semisimple Lie algebras and their representations; contains material rarely included in standard textbooks such as BGG resolution
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    Reviews & endorsements

    "The book is a very concise and nice introduction to Lie groups and Lie algebras. It seems to be well suited for a course on the subject. The exercises and examples will be useful in that case."
    Erik Koelink, Mathematical Reviews

    "I strongly recommend this book as a possible selection for graduate course(s), as well as independent study, or individual reading."
    Mihaela Poplicher, MAA Reviews

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    Product details

    • Date Published: April 2017
    • format: Paperback
    • isbn: 9781316614105
    • length: 234 pages
    • dimensions: 230 x 153 x 14 mm
    • weight: 0.36kg
    • availability: Available
  • Table of Contents

    Preface
    1. Introduction
    2. Lie groups: basic definitions
    3. Lie groups and Lie algebras
    4. Representations of Lie groups and Lie algebras
    5. Structure theory of Lie algebras
    6. Complex semisimple Lie algebras
    7. Root systems
    8. Representations of semisimple Lie Algebras
    Overview of the literature
    A. Root systems and simple Lie algebras
    B. Sample syllabus
    List of notation
    Index
    Bibliography.

  • Resources for

    An Introduction to Lie Groups and Lie Algebras

    Alexander Kirillov, Jr

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  • Author

    Alexander Kirillov, Jr, State University of New York, Stony Brook
    Alexander Kirillov, Jr, is an Associate Professor in the Mathematics Department, State University of New York, Stony Brook. His research interests are representation theory, Lie algebras, quantum groups, affine Lie algebras and conformal field theory.

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