Lie Algebras: Theory and Algorithms

Front Cover
Elsevier, Feb 4, 2000 - Mathematics - 408 pages
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Chapter 1 Basic constructions
1
Chapter 2 On nilpotency and solvability
39
Chapter 3 Cartan subalgebras
57
Chapter 4 Lie algebras with nondegenerate Killing form
89
Chapter 5 The classification of the simple Lie algebras
143
Chapter 6 Universal enveloping algebras
219
Chapter 7 Finitely presented Lie algebras
257
Chapter 8 Representations of semisimple Lie algebras
311
Appendix A On associative algebras
363
Bibliography
379
Index of Symbols
387
Index of Terminology
389
Index of Algorithms
393
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information