rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Lie algebras
    sub title: theory and algorithms
  name:
    name part: De Graaf, Willem A.
    role:
      role term: creator
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    place:
      place term: Amsterdam
    place:
      place term: New York
    publisher: Elsevier
    date issued: 2000
    edition: 1st ed.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xii, 393 pages)
  abstract: 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 Poincaré-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.
  note: Willem A. de Graaf.
  note: Includes bibliographical references (pages 379-386) and index.
  subject:
    topic: Lie algebras
  subject:
    topic: Algèbres de Lie
  subject:
    topic: MATHEMATICS
    topic: Algebra
    topic: Linear
  subject:
    topic: Lie algebras
  subject:
    topic: Lie-algebra's
  subject:
    topic: Algoritmen
  classification: QA252.3 .D4 2000eb
  classification: 512/.55
  related item:
    title info:
      title: Lie algebras
    name:
      name part: De Graaf, Willem A.
    origin info:
      publisher: Amsterdam ; New York : Elsevier, 2000
      edition: 1st ed.
    identifier: (DLC) 99086891
    identifier: (OCoLC)43114263
  related item:
    title info:
      title: North-Holland mathematical library ; v. 56
  identifier: 9780444501165
  identifier: 0444501169
  identifier: 9780080535456
  identifier: 0080535453
  identifier: 122749:127728 Elsevier Science & Technology
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 070802
    record change date: 20260326150622.0
    record identifier: in00005731834
    language of cataloging:
      language term: eng