東華大學圖書館 |

Theory of transformation groups I = General properties of continuous transformation groups : a contemporary approach and translation /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theory of transformation groups I/ by Sophus Lie ; edited by Joel Merker.
Reminder of title:	General properties of continuous transformation groups : a contemporary approach and translation /
Author:	Lie, Sophus.
other author:	Merker, Joel.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2015.,
Description:	xv, 643 p. :ill., digital ;24 cm.
[NT 15003449]:	Part I Modern Presentation -- 1 Three Principles of Thought Governing the Theory of Lie -- 2 Local Transformation Equations and Essential Parameters -- 3 Fundamental Differential Equations for Finite Continuous Transformation Groups -- 4 One-Term Groups and Ordinary Differential -- Part II English Translation -- 5 Complete Systems of Partial Differential Equations -- 7 Determination of All Systems of Equations Which Admit Given Infinitesimal Transformations -- 8 Complete Systems Which Admit All Transformations of a One-term Group -- 9 Characteristic Relationships Between the Infinitesimal Transformations of a Group -- 10 Systems of Partial Differential Equations the General Solution of Which Depends Only Upon a Finite Number of Arbitrary Constants -- 11 The Defining Equations for the Infinitesimal Transformations of a Group -- 12 Determination of All Subgroups of an r-term Group -- 13 Transitivity, Invariants -- 14 Determination of All Systems of Equations Which Admit a Given r-term Group -- 15 Invariant Families of Infinitesimal Transformations -- 16 The Adjoint Group -- 17 Composition and Isomorphism -- 18 Finite Groups, the Transformations of Which Form Discrete Continuous Families -- 19 Theory of the Similarity [AEHNLICHKEIT] of r-term Groups -- 20 Groups, the Transformations of Which Are Interchangeable With All Transformations of a Given Group -- 21 The Group of Parameters -- 22 The Determination of All r-term Groups -- 23 Invariant Families of Manifolds -- 24 Systatic and Asystatic Transformation Groups -- 25 Differential Invariants -- 26 The General Projective Group -- 27 Linear Homogeneous Groups -- 28 Approach [ANSATZ] towards the Determination of All Finite Continuous Groups of the n-times Extended Space -- 29 Characteristic Properties of the Groups Which are Equivalent to Certain Projective Groups -- Glossary of significantly used words -- Index.
Contained By:	Springer eBooks
Subject:	Transformation groups. -
Online resource:	http://dx.doi.org/10.1007/978-3-662-46211-9
ISBN:	9783662462119 (electronic bk.)

Theory of transformation groups I = General properties of continuous transformation groups : a contemporary approach and translation /
Lie, Sophus.

Theory of transformation groups IGeneral properties of continuous transformation groups : a contemporary approach and translation /[electronic resource] :by Sophus Lie ; edited by Joel Merker. - Berlin, Heidelberg :Springer Berlin Heidelberg :2015. - xv, 643 p. :ill., digital ;24 cm.

Part I Modern Presentation -- 1 Three Principles of Thought Governing the Theory of Lie -- 2 Local Transformation Equations and Essential Parameters -- 3 Fundamental Differential Equations for Finite Continuous Transformation Groups -- 4 One-Term Groups and Ordinary Differential -- Part II English Translation -- 5 Complete Systems of Partial Differential Equations -- 7 Determination of All Systems of Equations Which Admit Given Infinitesimal Transformations -- 8 Complete Systems Which Admit All Transformations of a One-term Group -- 9 Characteristic Relationships Between the Infinitesimal Transformations of a Group -- 10 Systems of Partial Differential Equations the General Solution of Which Depends Only Upon a Finite Number of Arbitrary Constants -- 11 The Defining Equations for the Infinitesimal Transformations of a Group -- 12 Determination of All Subgroups of an r-term Group -- 13 Transitivity, Invariants -- 14 Determination of All Systems of Equations Which Admit a Given r-term Group -- 15 Invariant Families of Infinitesimal Transformations -- 16 The Adjoint Group -- 17 Composition and Isomorphism -- 18 Finite Groups, the Transformations of Which Form Discrete Continuous Families -- 19 Theory of the Similarity [AEHNLICHKEIT] of r-term Groups -- 20 Groups, the Transformations of Which Are Interchangeable With All Transformations of a Given Group -- 21 The Group of Parameters -- 22 The Determination of All r-term Groups -- 23 Invariant Families of Manifolds -- 24 Systatic and Asystatic Transformation Groups -- 25 Differential Invariants -- 26 The General Projective Group -- 27 Linear Homogeneous Groups -- 28 Approach [ANSATZ] towards the Determination of All Finite Continuous Groups of the n-times Extended Space -- 29 Characteristic Properties of the Groups Which are Equivalent to Certain Projective Groups -- Glossary of significantly used words -- Index.

This modern translation of Sophus Lie's and Friedrich Engel's "Theorie der Transformationsgruppen Band I" will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations, and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

ISBN: 9783662462119 (electronic bk.)

Standard No.: 10.1007/978-3-662-46211-9doiSubjects--Topical Terms:

664493
Transformation groups.

LC Class. No.: QA387

Dewey Class. No.: 512.55

Theory of transformation groups I = General properties of continuous transformation groups : a contemporary approach and translation /
LDR:04422nmm a2200325 a 4500 001 1998087
003 DE-He213
005 20151029103346.0
006 m d
007 cr nn 008maaau
008 151112s2015 gw s 0 eng d
020 $a 9783662462119 (electronic bk.)
020 $a 9783662462102 (paper)
024 7 $a 10.1007/978-3-662-46211-9 $2 doi
035 $a 978-3-662-46211-9
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA387
072 7 $a PBG $2 bicssc
072 7 $a MAT014000 $2 bisacsh
072 7 $a MAT038000 $2 bisacsh
082 0 4 $a 512.55 $2 23
090 $a QA387 $b .L716 2015
100 1 $a Lie, Sophus. $3 2139600
245 1 0 $a Theory of transformation groups I $h [electronic resource] : $b General properties of continuous transformation groups : a contemporary approach and translation / $c by Sophus Lie ; edited by Joel Merker.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2015.
300 $a xv, 643 p. : $b ill., digital ; $c 24 cm.
505 0 $a Part I Modern Presentation -- 1 Three Principles of Thought Governing the Theory of Lie -- 2 Local Transformation Equations and Essential Parameters -- 3 Fundamental Differential Equations for Finite Continuous Transformation Groups -- 4 One-Term Groups and Ordinary Differential -- Part II English Translation -- 5 Complete Systems of Partial Differential Equations -- 7 Determination of All Systems of Equations Which Admit Given Infinitesimal Transformations -- 8 Complete Systems Which Admit All Transformations of a One-term Group -- 9 Characteristic Relationships Between the Infinitesimal Transformations of a Group -- 10 Systems of Partial Differential Equations the General Solution of Which Depends Only Upon a Finite Number of Arbitrary Constants -- 11 The Defining Equations for the Infinitesimal Transformations of a Group -- 12 Determination of All Subgroups of an r-term Group -- 13 Transitivity, Invariants -- 14 Determination of All Systems of Equations Which Admit a Given r-term Group -- 15 Invariant Families of Infinitesimal Transformations -- 16 The Adjoint Group -- 17 Composition and Isomorphism -- 18 Finite Groups, the Transformations of Which Form Discrete Continuous Families -- 19 Theory of the Similarity [AEHNLICHKEIT] of r-term Groups -- 20 Groups, the Transformations of Which Are Interchangeable With All Transformations of a Given Group -- 21 The Group of Parameters -- 22 The Determination of All r-term Groups -- 23 Invariant Families of Manifolds -- 24 Systatic and Asystatic Transformation Groups -- 25 Differential Invariants -- 26 The General Projective Group -- 27 Linear Homogeneous Groups -- 28 Approach [ANSATZ] towards the Determination of All Finite Continuous Groups of the n-times Extended Space -- 29 Characteristic Properties of the Groups Which are Equivalent to Certain Projective Groups -- Glossary of significantly used words -- Index.
520 $a This modern translation of Sophus Lie's and Friedrich Engel's "Theorie der Transformationsgruppen Band I" will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations, and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.
650 0 $a Transformation groups. $3 664493
650 0 $a Lie algebras. $3 526115
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Topological Groups, Lie Groups. $3 891005
650 2 4 $a Projective Geometry. $3 2056109
650 2 4 $a History of Mathematical Sciences. $3 1530523
700 1 $a Merker, Joel. $3 2139601
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-662-46211-9
950 $a Mathematics and Statistics (Springer-11649)