| Edition |
1st ed. |
| Description |
1 online resource (xii, 393 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematical library ; v. 56 |
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North-Holland mathematical library ; v. 56.
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| Summary |
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. |
| 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. |
| Bibliography |
Includes bibliographical references (pages 379-386) and index. |
| Note |
Print version record. |
| Subject |
Lie algebras.
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Algèbres de Lie.
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MATHEMATICS -- Algebra -- Linear.
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Lie algebras
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Lie-algebra's.
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Algoritmen.
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| Other Form: |
Print version: De Graaf, Willem A. Lie algebras. 1st ed. Amsterdam ; New York : Elsevier, 2000 0444501169 9780444501165 (DLC) 99086891 (OCoLC)43114263 |
| ISBN |
9780444501165 |
|
0444501169 |
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9780080535456 |
|
0080535453 |
| Standard No. |
AU@ 000048130055 |
|
AU@ 000062578825 |
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CHNEW 001005849 |
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DEBBG BV036962266 |
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DEBBG BV042317280 |
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DEBSZ 276236076 |
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DEBSZ 482352922 |
|
NZ1 12432961 |
|
NZ1 15192842 |
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UKMGB 017548806 |
|
