Theory of Transformation Groups I

Table of Contents

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   Book Overview
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   Chapter 1 Three Principles of Thought Governing the Theory of Lie
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   Chapter 2 Local Transformation Equations and Essential Parameters
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   Chapter 3 Fundamental Differential Equations for Finite Continuous Transformation Groups
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   Chapter 4 One-Term Groups and Ordinary Differential Equations
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   Chapter 5 Complete Systems of Partial Differential Equations
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   Chapter 6 New Interpretation of the Solutions of a Complete System
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   Chapter 7 Determination of All Systems of Equations Which Admit Given Infinitesimal Transformations
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   Chapter 8 Complete Systems Which Admit All Transformations of a One-term Group
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    Chapter 9 Characteristic Relationships Between the Infinitesimal Transformations of a Group
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    Chapter 10 Systems of Partial Differential Equations the General Solution of Which Depends Only Upon a Finite Number of Arbitrary Constants
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    Chapter 11 The Defining Equations for the Infinitesimal Transformations of a Group
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    Chapter 12 Determination of All Subgroups of an $$r$$ r -term Group
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    Chapter 13 Transitivity, Invariants, Primitivity
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    Chapter 14 Determination of All Systems of Equations Which Admit a Given $$r$$ r -term Group
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    Chapter 15 Invariant Families of Infinitesimal Transformations
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    Chapter 16 The Adjoint Group
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    Chapter 17 Composition and Isomorphism
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    Chapter 18 Finite Groups, the Transformations of Which Form Discrete Continuous Families
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    Chapter 19 Theory of the Similarity [Aehnlichkeit] of $$r$$ r -term Groups
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    Chapter 20 Groups, the Transformations of Which Are Interchangeable with All Transformations of a Given Group
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    Chapter 21 The Group of Parameters
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    Chapter 22 The Determination of All $$r$$ r -term Groups
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    Chapter 23 Invariant Families of Manifolds
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    Chapter 24 Systatic and Asystatic Transformation Groups
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    Chapter 25 Differential Invariants
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    Chapter 26 The General Projective Group
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    Chapter 27 Linear Homogeneous Groups
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    Chapter 28 Approach [Ansatz] Towards the Determination of All Finite Continuous Groups of $$n$$ n -times Extended Space
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    Chapter 29 Characteristic Properties of the Groups Which Are Equivalent to Certain Projective Groups