Theory of Transformation Groups I
General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation
Authors: Lie, Sophus
Editors: Merker, Joel (Ed.)
Free Preview- Revalues the purity and the incredible beauty of Lie’s architectural Theorie der Transformations gruppen
- Makes available Lie’s classification theorems that are not reproved in any modern textbook
- Offers to researchers the domain of PDEs' symmetries and the classification of differential equations in several (in)dependent variables
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- About this book
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This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen 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.
- About the authors
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Professor Joël Merker studied Mathematics and Philosophy at the Ecole Normale Supérieure in Paris where he received his Ph. D. in Mathematics (1996), followed by his habilitation in Mathematics (2006) and Ph. D. in Philosophy (2012). He was a CNRS researcher (1997-2010) and is currently Professor of Mathematics at Paris-Sud-Orsay University.
- Table of contents (29 chapters)
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Three Principles of Thought Governing the Theory of Lie
Pages 3-12
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Local Transformation Equations and Essential Parameters
Pages 13-22
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Fundamental Differential Equations for Finite Continuous Transformation Groups
Pages 23-60
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One-Term Groups and Ordinary Differential Equations
Pages 61-91
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Complete Systems of Partial Differential Equations
Pages 95-110
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Table of contents (29 chapters)
- Download Sample pages 2 PDF (228 KB)
- Download Table of contents PDF (177.7 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Theory of Transformation Groups I
- Book Subtitle
- General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation
- Authors
-
- Sophus Lie
- Editors
-
- Joel Merker
- Translated by
- Merker, J.
- Copyright
- 2015
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-662-46211-9
- DOI
- 10.1007/978-3-662-46211-9
- Hardcover ISBN
- 978-3-662-46210-2
- Softcover ISBN
- 978-3-662-51266-1
- Edition Number
- 1
- Number of Pages
- XV, 643
- Number of Illustrations
- 7 illustrations in colour
- Topics
