4 Lie algebras of operators

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变换群和李代数（英文版) (Transformation Groups and 作者：Nail Ibragimov　　 ISBN：978-7-04-036741-6　出版时间：2013-03-11

全书目录
本章目录

内封

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目录

Front Matter

Part I Local Transformation Groups

1 Preliminaries

2 One-parameter groups and their invariants

3 Groups admitted by differential equations

4 Lie algebras of operators

5 Galois groups via symmetries

Assignment to Part I

Part II Approximate Transformation Groups

6 Preliminaries

7 Approximate transformations

8 Approximate symmetries

9 Applications

Assignment to Part II

Bibliography

Index
- 4.1 Basic definitions
- 4.1.1 Commutator
- 4.1.2 Properties of the commutator
- 4.1.3 Properties of determining equations
- 4.1.4 Lie algebras
- 4.2 Basic properties
- 4.2.1 Notation
- 4.2.2 Subalgebra and ideal
- 4.2.3 Derived algebras
- 4.2.4 Solvable Lie algebras
- 4.3 Isomorphism and similarity
- 4.3.1 Isomorphic Lie algebras
- 4.3.2 Similar Lie algebras
- 4.4 Low-dimensional Lie algebras
- 4.4.1 One-dimensional algebras
- 4.4.2 Two-dimensional algebras in the plane
- 4.4.3 Three-dimensional algebras in the plane
- 4.4.4 Three-dimensional algebras in IR3
- 4.5 Lie algebras and multi-parameter groups
- 4.5.1 Definition of multi-parameter groups
- 4.5.2 Construction of multi-parameter groups
- Exercises to Chapter 4

4 Lie algebras of operators

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