LIE ALGEBRAS: THEORY AND ALGORITHMSNORTH HOLLAND MATHEMATICAL LIBRARY VOLUME 56 - Hardcover

 
9780444501165: LIE ALGEBRAS: THEORY AND ALGORITHMSNORTH HOLLAND MATHEMATICAL LIBRARY VOLUME 56
Hardcover
ISBN 10: 0444501169 ISBN 13: 9780444501165
Verlag: Elsevier, 2000

Inhaltsangabe

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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Críticas

....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

Reseña del editor

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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Verlag
Elsevier
Erscheinungsdatum
2000
Sprache
Englisch
ISBN 10 
0444501169
ISBN 13 
9780444501165
Einband
Tapa dura
Anzahl der Seiten
408
Herausgeber
Sevenster Arjen
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar