Constructions of Lie Algebras and their Modules

  • Authors
  • George¬†B.¬†Seligman

Part of the Lecture Notes in Mathematics book series (LNM, volume 1300)

Table of contents

  1. Front Matter
    Pages I-VI
  2. George B. Seligman
    Pages 1-11
  3. George B. Seligman
    Pages 12-20
  4. George B. Seligman
    Pages 179-185
  5. Back Matter
    Pages 186-195

About this book

Introduction

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.

Keywords

algebra associative algebra clifford algebra field lie algebra quadratic form

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0079295
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18973-2
  • Online ISBN 978-3-540-38864-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book