Lie Algebras: Theory and Algorithms - Couverture rigide

De Graaf, W.A.

 
9780444501165: Lie Algebras: Theory and Algorithms
Couverture rigide
ISBN 10 : 0444501169 ISBN 13 : 9780444501165
Editeur : North-Holland, 2000

Synopsis

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.

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Présentation de l'éditeur

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.

Revue de presse

....a book that will be useful for experts, as well as for interested researchers from other fields of mathematical physics.
European Mathematical Society Newsletter
This book presents both the Lie algebra theory and algorithms for computing much of the basic structure of Lie algebras. It is one of the first books which combines both these aspects in one volume. The book is well written and the material is clearly presented.
Mathematical Reviews

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
North-Holland
Date d'édition
2000
Langue
anglais
ISBN 10 
0444501169
ISBN 13 
9780444501165
Reliure
Relié
Nombre de pages
408
Coordonnées du fabricant
non disponible
Personne responsable
non disponible