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Constructions of Lie Algebras and their Modules

  • Book
  • © 1988

Overview

Authors:
  1. George B. Seligman
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1300)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-VI
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  2. An introductory example: sl(n,D)

    • George B. Seligman
    Pages 1-11

  3. General considerations

    • George B. Seligman
    Pages 12-20

  4. Involutorial algebras and modules for their skew elements

    • George B. Seligman
    Pages 21-36

  5. Construction of modules with prescribed relative highest weights, for the isotropic algebras of chapter 3

    • George B. Seligman
    Pages 37-51

  6. Construction of exceptional algebras from quadratic forms

    • George B. Seligman
    Pages 52-83

  7. Representations of exceptional algebras constructed from quadratic forms

    • George B. Seligman
    Pages 84-114

  8. Non-reduced excepticnal algebras with a one-dimensional root space

    • George B. Seligman
    Pages 115-140

  9. Construction of modules for the super-exceptional algebras of rank one

    • George B. Seligman
    Pages 141-178

  10. Complements

    • George B. Seligman
    Pages 179-185

  11. Back Matter

    Pages 186-195
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Keywords

About this book

This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.

Bibliographic Information

  • Book Title: Constructions of Lie Algebras and their Modules

  • Authors: George B. Seligman

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0079295

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-18973-2Published: 09 March 1988

  • eBook ISBN: 978-3-540-38864-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 196

  • Topics: Topological Groups, Lie Groups

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