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Theory of Transformation Groups I - General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation (Paperback, Softcover reprint of the original 1st ed. 2015)
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Theory of Transformation Groups I - General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation (Paperback, Softcover reprint of the original 1st ed. 2015)
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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.
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