UID:
almahu_9949698063002882
Format:
1 online resource (407 p.)
Edition:
1st ed.
ISBN:
1-281-04825-9
,
9786611048259
,
0-08-053545-3
Series Statement:
North-Holland mathematical library ; v. 56
Content:
〈![CDATA[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 straightforwar
Note:
Description based upon print version of record.
,
Front Cover; Lie Algebras: Theory and Algorithms; Copyright Page; Contents; Chapter 1. Basic constructions; 1.1 Algebras: associative and Lie; 1.2 Linear Lie algebras; 1.3 Structure constants; 1.4 Lie algebras from p-groups; 1.5 On algorithms; 1.6 Centralizers and normalizers; 1.7 Chains of ideals; 1.8 Morphisms of Lie algebras; 1.9 Derivations; 1.10 (Semi)direct sums; 1.11 Automorphisms of Lie algebras; 1.12 Representations of Lie algebras; 1.13 Restricted Lie algebras; 1.14 Extension of the ground field; 1.15 Finding a direct sum decomposition; 1.16 Notes
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Chapter 2. On nilpotency and solvability2.1 Engel's theorem; 2.2 The nilradical; 2.3 The solvable radical; 2.4 Lie's theorems; 2.5 A criterion for solvability; 2.6 A characterization of the solvable radical; 2.7 Finding a non-nilpotent element; 2.8 Notes; Chapter 3. Cartan subalgebras; 3.1 Primary decompositions; 3.2 Cartan subalgebras; 3.3 The root space decomposition; 3.4 Polynomial functions; 3.5 Conjugacy of Cartan subalgebras; 3.6 Conjugacy of Cartan subalgebras of solvable Lie algebras; 3.7 Calculating the nilradical; 3.8 Notes; Chapter 4. Lie algebras with non-degenerate Killing form
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4.1 Trace forms and the Killing form4.2 Semisimple Lie algebras; 4.3 Direct sum decomposition; 4.4 Complete reducibility of representations; 4.5 All derivations are inner; 4.6 The Jordan decomposition; 4.7 Levi's theorem; 4.8 Existence of a Cartan subalgebra; 4.9 Facts on roots; 4.10 Some proofs for modular fields; 4.11 Splitting and decomposing elements; 4.12 Direct sum decomposition; 4.13 Computing a Levi subalgebra; 4.14 A structure theorem of Cartan subalgebras; 4.15 Using Cartan subalgebras to compute Levi subalgebras; 4.16 Notes; Chapter 5. The classification of the simple Lie algebras
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5.1 Representations of sI2(F)5.2 Some more root facts; 5.3 Root systems; 5.4 Root systems of rank two; 5.5 Simple systems; 5.6 Cartan matrices; 5.7 Simple systems and the Weyl group; 5.8 Dynkin diagrams; 5.9 Classifying Dynkin diagrams; 5.10 Constructing the root systems; 5.11 Constructing isomorphisms; 5.12 Constructing the semisimple Lie algebras; 5.13 The simply-laced case; 5.14 Diagram automorphisms; 5.15 The non simply-laced case; 5.16 Thc classification theorem; 5.17 Recognizing a semisimple Lie algebra; 5.18 Notes; Chapter 6. Universal enveloping algebras
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6.1 Ideals in free associative algebras6.2 Universal enveloping algebras; 6.3 Gröbner bases in universal enveloping algebras; 6.4 Gröbner bases of left ideals; 6.5 Constructing a representation of a Lie algebra of characteristic 0; 6.6 The theorem of Iwasawa; 6.7 Notes; Chapter 7. Finitely presented Lie algebras; 7.1 Free Lie algebras; 7.2 Finitely presented Lie algebras; 7.3 Gröbner bases in free algebras; 7.4 Constructing a basis of a finitely presented Lie algebra; 7.5 Hall sets; 7.6 Standard sequences; 7.7 A Hall set provides a basis; 7.8 Two examples of Hall orders; 7.9 Reduction in L(X)
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7.10 Gröbner bases in free Lie algebras
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English
Additional Edition:
ISBN 0-444-50116-9
Language:
English
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