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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.
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.
In diesem Monat feiern wir den 150. Geburtstag von SOPHUS LIE,
einem der groessten Mathematiker des vorigen Jahrhunderts. Es ist
daher sehr zu begrussen, dass der Teubner Verlag, einer langen
Traditionslinie bei der Veroeffentlichung von LIES Werken folgend,
in seine Reihe "TEUBNER-ARCHIV zur Mathematik" Arbeiten von SOPHUS
LIE und seinen Zeitgenossen EDuARD STUDY und FRIEDRICH ENGEL
aufgenommen hat. Ausgewahlt wurden Beitrage zur Theorie der
Differentialinvarianten. Zum einen ist dies ein Gebiet, auf dem
alle drei tatig gewesen sind und das als Ausgangspunkt grosser
Liescher Ideen zur Anwendung gruppentheoretischer Methoden in der
Analysis betrachtet werden kann, obwohl es nur einen Ausschnitt aus
LIES Schaffen darstellt. Zum anderen vermitteln die hier
vorgestellten Arbeiten durch ihren kritischen Stil und durch den
Streit um unterschied liche mathematische Auffassungen interessante
Einblicke in das mathematische Geschehen jener Zeit. Neben der
Wurdigung dieser drei namhaften Mathematiker stellt der vorliegende
Band den Ursprung der Lieschen Theorie, ihre weitere Entwicklung
und spatere Auspragung dar. Wir danken dem Teubner-Verlag und
insbesondere Herrn J. WEISS fur das freundliche Entgegenkommen und
die gute Zusammenarbeit. Greifswald und Leipzig, Dezember 1992
GUENTER CZICHOWSKI BERND FRITZSCHE SOPHUS LIE OElgemalde von ERIK
THEODOR WERENSKIOLD aus dem Jahre 1902; im Besitz der Universitat
Oslo (Katalognummer 818) Inhalt S. Lie: UEber Gruppen von
Transformationen, 1874. (Gesammelte Abhandlungen, Bd. 5 (1924),1-8)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 S. Lie: UEber Differentialinvarianten, 1884. (Gesammelte
Abhandlungen, Bd. 6 (1927), 95-l38) . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 16 . . . . . . . S. Lie: UEber die Gruppe
der Bewegungen und ihre Differentialinvarianten, 1893. (Gesammelte
Abhandlungen, Bd. 6 (1927), 376-383) . . . . . . . . . . . . . . .
Das Halten einer Antrittsvorlesung gehArte zu den bewAhrten
Traditionen der deutschen UniversitAten. Diese Reden spiegelten in
der Regel die Ansichten des Neuberufenen zu allgemeinen Fragen
seiner Wissenschaft wider, nicht selten auch programmatische
Vorstellungen A1/4ber das zukA1/4nftige Wirken. Sie waren so
gehalten, daA sie einem breiten Publikum verstAndlich blieben. Die
vorliegende Sammlung Leipziger mathematischer Antrittsvorlesungen
der Jahre 1869 bis 1922 enthAlt fotomechanische Nachdrucke der
entsprechenden Reden von Carl Neumann, Felix Klein, Sophus Lie,
Friedrich Engel, Felix Hausdorff, Heinrich Liebmann, Wilhelm
Blaschke und Leon Lichtenstein. Das Buch wird ergAnzt durch kurze
Biographien dieser Gelehrten sowie durch einige aufschluAreiche,
teilweise noch unverAffentlichte Archivalien.
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
++++ The below data was compiled from various identification fields
in the bibliographic record of this title. This data is provided as
an additional tool in helping to ensure edition identification:
++++ Vorlesungen �ber Die Integration Der Partiellen
Differentialgleichungen Erster Ordnung Edouard Goursat, Sophus Lie,
C. Bourlet, H. Maser B. G. Teubner, 1893 Differential equations;
Differential equations, Partial
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
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