Lie algebras : theory and algorithms

Bibliographic Information

Lie algebras : theory and algorithms

Willem A. de Graaf

(North-Holland mathematical library, v. 56)

Elsevier, 2000

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Note

Includes bibliographical references (p. [379]-386) and index

Description and Table of Contents

Description

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincare-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Table of Contents

Basic constructions. On nilpotency and colvability. Cartan subalgebras. Lie algebras with non-degenerate Killing form. The classification of the simple Lie algebras. Universal enveloping algebras. Finitely presented Lie algebras. Representations of semisimple Lie algebras. On associative algebras. Bibliography. Index of Symbols. Index of Terminology. Index of Algorithms.

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Details

  • NCID
    BA45541914
  • ISBN
    • 0444501169
  • LCCN
    99086891
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Amsterdam
  • Pages/Volumes
    xii, 393 p.
  • Size
    23 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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